DIMPLE PATTERNS FOR GOLF BALLS

Description

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation-in-Part of co-pending U.S. patent application Ser. No. 13/672,910, filed Nov. 9, 2012, which is a Continuation-in-Part of U.S. patent application Ser. No. 13/251,590, filed Oct. 3, 2011, now abandoned, which is a Divisional of U.S. patent application Ser. No. 12/262,464 filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the disclosures of which are incorporated by reference herein in their entirety.

FIELD OF THE INVENTION

This invention relates to golf balls, particularly to golf balls having improved dimple patterns. More particularly, the invention relates to methods of arranging dimples on a golf ball by generating irregular domains based on polyhedrons, packing the irregular domains with dimples, and tessellating the domains onto the surface of the golf ball. Still more particularly, this invention relates to dimple patterns with icosahedral tilings wherein there exists a sub-pattern of dimples that are additionally tiled around the ball such that the sub-pattern dimples exhibit a different plan shape or dimple profile than the other dimples on the golf ball.

BACKGROUND OF THE INVENTION

Historically, dimple patterns for golf balls have had a variety of geometric shapes, patterns, and configurations. Primarily, patterns are laid out in order to provide desired performance characteristics based on the particular ball construction, material attributes, and player characteristics influencing the ball's initial launch angle and spin conditions. Therefore, pattern development is a secondary design step that is used to achieve the appropriate aerodynamic behavior, thereby tailoring ball flight characteristics and performance.

Aerodynamic forces generated by a ball in flight are a result of its velocity and spin. These forces can be represented by a lift force and a drag force. Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus, who described it in 1853 after studying the aerodynamic forces on spinning spheres and cylinders, and is described by Bernoulli's Equation, a simplification of the first law of thermodynamics. Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom, results in lower air pressure on top and an upward directed force on the ball.

Drag is opposite in sense to the direction of flight and orthogonal to lift. The drag force on a ball is attributed to parasitic drag forces, which consist of pressure drag and viscous or skin friction drag. A sphere is a bluff body, which is an inefficient aerodynamic shape. As a result, the accelerating flow field around the ball causes a large pressure differential with high-pressure forward and low-pressure behind the ball. The low pressure area behind the ball is also known as the wake. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind the ball. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer. The industry has seen many efforts to maximize the aerodynamics of golf balls, through dimple disturbance and other methods, though they are closely controlled by golf's national governing body, the United States Golf Association (U.S.G.A.). One U.S.G.A. requirement is that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with a very small amount of variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.

In attempts to improve aerodynamic symmetry, many dimple patterns are based on geometric shapes. These may include circles, hexagons, triangles, and the like. Other dimple patterns are based in general on the five Platonic Solids including icosahedron, dodecahedron, octahedron, cube, or tetrahedron. Yet other dimple patterns are based on the thirteen Archimedean Solids, such as the small icosidodecahedron, rhomicosidodecahedron, small rhombicuboctahedron, snub cube, snub dodecahedron, or truncated icosahedron. Furthermore, other dimple patterns are based on hexagonal dipyramids. Because the number of symmetric solid plane systems is limited, it is difficult to devise new symmetric patterns. Moreover, dimple patterns based some of these geometric shapes result in less than optimal surface coverage and other disadvantageous dimple arrangements. Therefore, dimple properties such as number, shape, size, and arrangement are often manipulated in an attempt to generate a golf ball that has better aerodynamic properties.

U.S. Pat. No. 5,562,552 to Thurman discloses a golf ball with an icosahedral dimple pattern, wherein each triangular face of the icosahedron is split by a three straight lines which each bisect a corner of the face to form 3 triangular faces for each icosahedral face, wherein the dimples are arranged consistently on the icosahedral faces.

U.S. Pat. No. 5,046,742 to Mackey discloses a golf ball with dimples packed into a 32-sided polyhedron composed of hexagons and pentagons, wherein the dimple packing is the same in each hexagon and in each pentagon.

U.S. Pat. No. 4,998,733 to Lee discloses a golf ball formed of ten “spherical” hexagons each split into six equilateral triangles, wherein each triangle is split by a bisecting line extending between a vertex of the triangle and the midpoint of the side opposite the vertex, and the bisecting lines are oriented to achieve improved symmetry.

U.S. Pat. No. 6,682,442 to Winfield discloses the use of polygons as packing elements for dimples to introduce predictable variance into the dimple pattern. The polygons extend from the poles of the ball to a parting line. Any space not filled with dimples from the polygons is filled with other dimples. A continuing need exists for a dimple pattern whose dimple arrangement results in a maximized surface coverage and desirable aerodynamic characteristics, including improved symmetry.

SUMMARY OF THE INVENTION

The present invention provides a method for arranging dimples on a golf ball surface that significantly improves aerodynamic symmetry and minimizes parting line visibility by arranging the dimples in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. The method includes choosing control points of a polyhedron, generating an irregular domain based on those control points, packing the irregular domain with dimples, and tessellating the irregular domain to cover the surface of the golf ball.

One embodiment of the present invention provides for an initial dimple sub-pattern contained in the irregular domain(s). The dimple sub-pattern may be defined as nearest neighbor dimples on or within edges of one or more of the irregular domains. Once the sub-pattern is defined, the remaining unpacked spherical region is packed with dimples around the initial sub-pattern of dimples. The irregular domains are then tessellated around the ball surface. The sub-pattern dimples can be packed within any number of the irregular domains.

The method of determining nearest neighbor dimples is illustrated in FIG. 11C, wherein two tangency lines TL are drawn from the center of a first dimple to a potential nearest neighbor dimple. Additionally, a line segment Ls is drawn connecting the center of the first dimple to the center of the potential nearest neighbor dimple. If there is no line segment that is intersected by another dimple, or portion of a dimple, then those dimples are considered to be nearest neighbor dimples.

The golf ball produced by the method of the present invention has a sub-pattern of nearest neighbor dimples that are visually distinct from the other packed dimples. The sub-pattern of nearest neighbor dimples may exhibit different perimeter shape, or dimple profile, or color, or texture, or grooves, or brambles or a combination therein from the packed dimples of the initial base geometry. The sub-pattern of nearest neighbor dimples may have circular perimeters with diameters ranging between 0.100 to 0.220 inches. In golf balls wherein the sub-pattern of nearest neighbor dimples have non-circular perimeters; the diameter range is between 0.120 to 0.270 inches when the non-circular perimeters are circumscribed by a circle.

The present invention provides for a golf ball wherein each sub-pattern contains 2 to 80 nearest neighbor dimples, and wherein the base geometry of each irregular domain contains 10 to 115 dimples. The surface coverage of dimples is between 70 to 90 percent, including surface coverage of sub-pattern nearest neighbor dimples between 10 to 60 percent.

Other embodiments of the present invention may have dimple profiles that are spherical, Gabriel's horn, catenary, conical, Witch of Agnesi, ellipse, or any other profile defined by the superposition of two or more curves or spherically weighted profiles. Further these dimples can have perimeters such as circular, or polygonal, or elliptical.

The present invention is directed to a golf ball having an outer surface and comprising a plurality of dimples disposed thereon. The dimples are arranged in multiple copies of a first domain and a second domain, and the dimple pattern in the first domain is different than the dimple pattern in the second domain. The first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and being tessellated in an icosahedron pattern that consists of twenty first domains and twelve second domains.

A majority of dimples have a first plan shape and a first profile shape, and at least one of the domains has a sub-pattern of nearest neighbor dimples having either a plan shape or a dimple profile shape that is different than the majority of dimples.

The first domain has three-way rotational symmetry about a central point of the first domain and the second domain has five-way rotational symmetry about a central point of the second domain.

In one embodiment, the sub-pattern of nearest neighbor dimples are axially symmetric about the central point of one of the two domains. In another embodiment, the sub-pattern of nearest neighbor dimples have a different plan shape than the majority of dimples. For example, the majority of dimples may have a continuous plan shape and the sub-pattern dimples may have a plan shape that is discontinuous.

In another embodiment, the sub-pattern of nearest neighbor dimples have a different dimple plan shape than the majority of dimples. For example, the majority of dimples may have a circular plan shape. It will be appreciated that the sub-pattern of dimples may have a polygonal plan shape, or may have plan shapes based on periodic functions along a path or the sub-pattern of dimples may have plan shapes made of circular arcs derived from polygons.

In yet another embodiment, the sub-pattern of nearest neighbor dimples have a different dimple profile shape than the majority of dimples. For example, the majority of the dimples and the sub-pattern of dimples may be different and chosen from the group of spherical, conical, and catenary, and Gabriel's horn type dimple profiles.

In another embodiment, the majority of dimples may be spherical, while the sub-pattern may be conical or catenary dimples or chosen from the group of circumscribed prismatoids, rotational protrusions, frequency dimples, superposition dimples, Gabriel's horn dimples or grooved dimple profiles.

In yet another embodiment, the sub-pattern of dimples may all be classified as interior dimples within a domain. The interior dimples in one domain may be sub-pattern dimples. In another embodiment, the sub-pattern of dimples may all be classified as perimeter dimples within a domain. The perimeter dimples of one domain may be sub-pattern dimples.

It will be appreciated that in another embodiment, the sub-pattern of dimples may include both interior dimples and perimeter dimples within a domain. The sub-pattern dimples may be classified as perimeter dimples from the first domain and perimeter dimples from the second domain.

At least one sub-pattern dimple may be at the center of one domain, and it will be appreciated that there may be a sub-pattern dimple at the center of both domains.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views:

FIG. 1A illustrates a golf ball having dimples arranged by a method of the invention; FIG. 1B illustrates a polyhedron face; FIG. 1C illustrates an element of the invention in the polyhedron face of FIG. 1B; and FIG. 1D illustrates a domain formed by a methods of the invention packed with dimples and formed from two elements of FIG. 1C;

FIG. 2 illustrates a single face of a polyhedron having control points thereon;

FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates an element of the invention packed with dimples; FIG. 3C illustrates a domain of the invention packed with dimples formed from elements of FIG. 3B; and FIG. 3D illustrates a golf ball formed by a method of the invention formed of the domain of FIG. 3C;

FIG. 4A illustrates two polyhedron faces; FIG. 4B illustrates a first domain of the invention in the two polyhedron faces of FIG. 4A; FIG. 4C illustrates a first domain and a second domain of the invention in three polyhedron faces; FIG. 4D illustrates a golf ball formed by a method of the invention formed of the domains of FIG. 4C;

FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a first domain of the invention in a polyhedron face; FIG. 5C illustrates a first domain and a second domain of the invention in three polyhedron faces; and FIG. 5D illustrates a golf ball formed using a method of the invention formed of the domains of FIG. 5C;

FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a portion of a domain of the invention in the polyhedron face of FIG. 6A; FIG. 6C illustrates a domain formed by the methods of the invention; and FIG. 6D illustrates a golf ball formed using the methods of the invention formed of domains of FIG. 6C;

FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a domain of the invention in the polyhedron face of FIG. 7A; and FIG. 7C illustrates a golf ball formed by a method of the invention;

FIG. 8A illustrates a first element of the invention in a polyhedron face; FIG. 8B illustrates a first and a second element of the invention in the polyhedron face of FIG. 8A; FIG. 8C illustrates two domains of the invention composed of first and second elements of FIG. 8B; FIG. 8D illustrates a single domain of the invention based on the two domains of FIG. 8C; and FIG. 8E illustrates a golf ball formed using a method of the invention formed of the domains of FIG. 8D;

FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates an element of the invention in the polyhedron face of FIG. 9A; FIG. 9C illustrates two elements of FIG. 9B combining to form a domain of the invention; FIG. 9D illustrates a domain formed by the methods of the invention based on the elements of FIG. 9C; and FIG. 9E illustrates a golf ball formed using a method formed of domains of FIG. 9D;

FIG. 10A illustrates a face of a rhombic dodecahedron; FIG. 10B illustrates a segment of the present invention in the face of FIG. 10A; FIG. 10C illustrates the segment of FIG. 10B and copies thereof forming a domain of the present invention; FIG. 10D illustrates a domain formed by a method of the present invention based on the segments of FIG. 10C; and FIG. 10E illustrates a golf ball formed by a method of the present invention formed of domains of FIG. 10D;

FIG. 11A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 11B utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 11C depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

FIG. 11D depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of another of the irregular domains;

FIG. 11E shows the domains of FIG. 11C and FIG. 11D tessellated around a golf ball sphere;

FIG. 12A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 12B depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

FIG. 12C shows the domains of FIG. 12B tessellated around a golf ball sphere;

FIG. 13A depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

FIG. 13B shows the domains of FIG. 13A tessellated around a golf ball sphere;

FIG. 14A depicts first and second domains of the present invention; FIG. 14B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 14C illustrates a golf ball having the first and second domains of FIG. 14B tessellated on the surface of the golf ball; FIG. 14D depicts the cross-section of the majority of dimples showing the dimple profile; and FIG. 14E depicts the cross-section of the sub-pattern dimples showing the dimple profile;

FIG. 15A depicts first and second domains of the present invention; FIG. 15B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 15C illustrates a golf ball having the first and second domains of FIG. 15B tessellated on the surface of the golf ball; FIG. 15D depicts the cross-section of the majority of dimples showing the dimple profile; and FIG. 15E depicts the cross-section of the sub-pattern dimples showing the dimple profile; and

FIG. 16A depicts first and second domains of an embodiment of the present invention; FIG. 16B depicts a majority of dimples and sub-pattern dimples in the first and second domains of the present invention; FIG. 16C illustrates a golf ball having the first and second domains of FIG. 16B tessellated on the surface of the golf ball; FIG. 16D depicts the plan shape of the majority of dimples; and FIG. 16E depicts the plan shape of the sub-pattern dimples.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides a method for arranging dimples on a golf ball surface in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. In the invention as described below extends the method of spherical tiling to include sub-patterns of dimples within the base geometry dimple packing. Unique patterns are thus created with improved aerodynamics and visual aesthetics.

In one embodiment, illustrated in FIG. 1A, the present invention comprises a golf ball 10 comprising dimples 12. Dimples 12 are arranged by packing irregular domains 14 with dimples, as seen best in FIG. 1D. Irregular domains 14 are created in such a way that, when tessellated on the surface of golf ball 10, they impart greater orders of symmetry to the surface than prior art balls. The irregular shape of domains 14 additionally minimize the appearance and effect of the golf ball parting line from the molding process, and allows greater flexibility in arranging dimples than would be available with regularly shaped domains.

The irregular domains can be defined through the use of any one of the exemplary methods described herein. Each method produces one or more unique domains based on circumscribing a sphere with the vertices of a regular polyhedron. The vertices of the circumscribed sphere based on the vertices of the corresponding polyhedron with origin (0,0,0) are defined below in Table 1.

TABLE 1
Vertices of Circumscribed Sphere based
on Corresponding Polyhedron Vertices

Type of
Polyhedron	Vertices
Tetrahedron	(+1, +1, +1); (−1, −1, +1); (−1, +1, −1); (+1, −1, −1)
Cube	(±1, ±1, ±1)
Octahedron	(±1, 0, 0); (0, ±1, 0); (0, 0, ±1)
Dodecahedron	(±1, ±1, ±1); (0, ±1/φ, ±φ); (±1/φ, ±φ, 0); (±φ, 0, ±1/φ)*
Icosahedron	(0, ±1, ±φ); (±1, ±φ, 0); (±φ, 0, ±1)*
*φ = (1 + {square root over (5)})/2

Each method has a unique set of rules which are followed for the domain to be symmetrically patterned on the surface of the golf ball. Each method is defined by the combination of at least two control points. These control points, which are taken from one or more faces of a regular or non-regular polyhedron, consist of at least three different types: the center C of a polyhedron face; a vertex V of a face of a regular polyhedron; and the midpoint M of an edge of a face of the polyhedron. FIG. 2 shows an exemplary face 16 of a polyhedron (a regular dodecahedron in this case) and one of each a center C, a midpoint M, a vertex V, and an edge E on face 16.

The two control points C, M, or V may be of the same or different types. Accordingly, six types of methods for use with regular polyhedrons are defined as follows:

1. Center to midpoint (C→M);

2. Center to center (C→C);

3. Center to vertex (C→V);

4. Midpoint to midpoint (M→M);

5. Midpoint to Vertex (M→V); and

6. Vertex to Vertex (V→V).

While each method differs in its particulars, they all follow the same basic scheme. First, a non-linear sketch line is drawn connecting the two control points. This sketch line may have any shape, including, but not limited, to an arc, a spline, two or more straight or acute lines or curves, or a combination thereof. Second, the sketch line is patterned in a method specific manner to create a domain, as discussed below. Third, when necessary, the sketch line is patterned in a second fashion to create a second domain.

While the basic scheme is consistent for each of the six methods, each method preferably follows different steps in order to generate the domains from a sketch line between the two control points, as described below with reference to each of the methods individually.

The Center to Vertex Method

Referring again to FIGS. 1A-1D, the center to vertex method yields a domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 1A-1D use an icosahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 1B;
  • 3. Center C of face 16, and a first vertex V₁ of face 16 are connected with any non-linear sketch line, hereinafter referred to as a segment 18;
  • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with vertex V₂ adjacent to vertex V₁. The two segments 18 and 20 and the edge E connecting vertices V₁ and V₂ define an element 22, as shown best in FIG. 1C; and
  • 5. Element 22 is rotated about midpoint M of edge E to create a domain 14, as shown best in FIG. 1D.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 1A, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and V₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_F of the polyhedron chosen times the number of edges P_E per face of the polyhedron divided by 2, as shown below in Table 2.

TABLE 2: Domains Resulting from Use of Specific Polyhedra when Using the

TABLE 2
Domains Resulting Form Use of Specific Polyhedra When Using the
Center to Vertex Method

Type of	Number of Faces,	Number	Number of Domains
Polyhedron	PF	of Edges, PE	14

Tetrahedron	4	3	6
Cube	6	4	12
Octahedron	8	3	12
Dodecahedron	12	5	30
Icosahedron	20	3	30

The Center to Midpoint Method

Referring to FIGS. 3A-3D, the center to midpoint method yields a single irregular domain that can be tessellated to cover the surface of golf ball 10. The domain is defined as follows:

1. A regular polyhedron is chosen (FIGS. 3A-3D use a dodecahedron);

2. A single face 16 of the regular polyhedron is chosen, shown in FIG. 3A;

3. Center C of face 16, and midpoint M₁ of a first edge E₁ of face 16 are connected with a segment 18;

4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂ of a second edge E₂ adjacent to first edge E₁. The two segments 16 and 18 and the portions of edge E₁ and edge E₂ between midpoints M₁ and M₂ define an element 22; and

5. Element 22 is patterned about vertex V of face 16 which is contained in element 22 and connects edges E₁ and E₂ to create a domain 14.

When domain 14 is tessellated around a golf ball 10 to cover the surface of golf ball 10, as shown in FIG. 3D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and M₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of vertices P_v of the chosen polyhedron, as shown below in Table 3.

TABLE 3
Domains resulting from use of specific Polyhedra when using the
Center to Midpoint Method

Type of Polyhedron	Number of Vertices, PV	Number of Domains 14

Tetrahedron	4	4
Cube	8	8
Octahedron	6	6
Dodecahedron	20	20
Icosahedron	12	12

The Center to Center Method

Referring to FIGS. 4A-4D, the center to center method yields two domains that can be tessellated to cover the surface of golf ball 10. The domains are defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 4A-4D use a dodecahedron);
  • 2. Two adjacent faces 16a and 16b of the regular polyhedron are chosen, as shown in FIG. 4A;
  • 3. Center C₁ of face 16a, and center C₂ of face 16b are connected with a segment 18;
  • 4. A copy 20 of segment 18 is rotated 180 degrees about the midpoint M between centers C₁ and C₂, such that copy 20 also connects center C₁ with center C₂, as shown in FIG. 4B. The two segments 16 and 18 define a first domain 14a; and
  • 5. Segment 18 is rotated equally about vertex V to define a second domain 14b, as shown in FIG. 4C.

When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 4D, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points C₁ and C₂. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P_F*P_E/2 for first domain 14a and P_v for second domain 14b, as shown below in Table 4.

TABLE 4
Domains Resulting From Use of Specific Polyhedra When Using the
Center to Center Method

		Number of	Number		Number of
	Number of	First	of		Second
Type of	Vertices,	Domains	Faces,	Number of	Domains
Polyhedron	PV	14a	PF	Edges, PE	14b

Tetrahedron	4	6	4	3	4
Cube	8	12	6	4	8
Octahedron	6	9	8	3	6
Dodecahedron	20	30	12	5	20
Icosahedron	12	18	20	3	12

The Midpoint to Midpoint Method

Referring to FIGS. 5A-5D, the midpoint to midpoint method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 5A-5D use a dodecahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 5A;
  • 3. The midpoint M₁ of a first edge E₁ of face 16, and the midpoint M₂ of a second edge E₂ adjacent to first edge E₁ are connected with a segment 18;
  • 4. Segment 18 is patterned around center C of face 16 to form a first domain 14a, as shown in FIG. 5B;
  • 5. Segment 18, along with the portions of first edge E₁ and second edge E₂ between midpoints M₁ and M₂, define an element 22; and
  • 6. Element 22 is patterned about vertex V which is contained in element 22 and connects edges E₁ and E₂ to create a second domain 14b, as shown in FIG. 5C.

When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 5D, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points M₁ and M₂. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P_F for first domain 14a and P_v for second domain 14b, as shown below in Table 5.

TABLE 5
Domains resulting from use of specific polyhedra when using the
Center to Center Method

		Number	Number of	Number of
Type of	Number of	of First	Vertices,	Second Domains
Polyhedron	Faces, PF	Domains 14a	PV	14b

Tetrahedron	4	4	4	4
Cube	6	6	8	8
Octahedron	8	8	6	6
Dodecahedron	12	12	20	20
Icosahedron	20	20	12	12

The Midpoint to Vertex Method

Referring to FIGS. 6A-6D, the midpoint to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 6A-6D use a dodecahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 6A;
  • 3. A midpoint M₁ of edge E₁ of face 16 and a vertex V₁ on edge E₁ are connected with a segment 18;
  • 4. Copies 20 of segment 18 is patterned about center C of face 16, one for each midpoint M₂ and vertex V₂ of face 16, to define a portion of domain 14, as shown in FIG. 6B; and
  • 5. Segment 18 and copies 20 are then each rotated 180 degrees about their respective midpoints to complete domain 14, as shown in FIG. 6C.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 6D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M₁ and V₁. The number of domains 14 used to cover the surface of golf ball 10 is P_F, as shown in Table 6.

TABLE 6
Domains resulting from use of specific polyhedra when using the
Midpoint to Vertex Method

Type of Polyhedron	Number of Faces, PF	Number of Domains 14

Tetrahedron	4	4
Cube	6	6
Octahedron	8	8
Dodecahedron	12	12
Icosahedron	20	20

The Vertex to Vertex Method

Referring to FIGS. 7A-7C, the vertex to vertex method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 7A-7C use an icosahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 7A;
  • 3. A first vertex V₁ face 16, and a second vertex V₂ adjacent to first vertex V₁ are connected with a segment 18;
  • 4. Segment 18 is patterned around center C of face 16 to form a first domain 14a, as shown in FIG. 7B;
  • 5. Segment 18, along with edge E₁ between vertices V₁ and V₂, defines an element 22; and
  • 6. Element 22 is rotated around midpoint M₁ of edge E₁ to create a second domain 14b.

When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in FIG. 7C, a different number of total domains 14a and 14b will result depending on the regular polyhedron chosen as the basis for control points V₁ and V₂. The number of first and second domains 14a and 14b used to cover the surface of golf ball 10 is P_F for first domain 14a and P_F*P_E/2 for second domain 14b, as shown below in Table 7.

TABLE 7
Domains resulting from use of specific polyhedra when using the
Vertex to Vertex Method

				Number of
		Number	Number of	Second
Type of	Number of	of First	Edges per Face,	Domains
Polyhedron	Faces, PF	Domains 14a	PE	14b

Tetrahedron	4	4	3	6
Cube	6	6	4	12
Octahedron	8	8	3	12
Dodecahedron	12	12	5	30
Icosahedron	20	20	3	30

While the six methods previously described each make use of two control points, it is possible to create irregular domains based on more than two control points. For example, three, or even more, control points may be used. The use of additional control points allows for potentially different shapes for irregular domains. An exemplary method using a midpoint M, a center C and a vertex V as three control points for creating one irregular domain is described below.

The Midpoint to Center to Vertex Method

Referring to FIGS. 8A-8E, the midpoint to center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 8A-8E use an icosahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 8A;
  • 3. A midpoint M₁ on edge E₁ of face 16, Center C of face 16 and a vertex V₁ on edge E₁ are connected with a segment 18, and segment 18 and the portion of edge E₁ between midpoint M₁ and vertex V₁ define a first element 22a, as shown in FIG. 8A;
  • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂ on edge E₂ adjacent to edge E₁, and connects center C with a vertex V₂ at the intersection of edges E₁ and E₂, and the portion of segment 18 between midpoint M₁ and center C, the portion of copy 20 between vertex V₂ and center C, and the portion of edge E₁ between midpoint M₁ and vertex V₂ define a second element 22b, as shown in FIG. 8B;
  • 5. First element 22a and second element 22b are rotated about midpoint M₁ of edge E₁, as seen in FIG. 8C, to define two domains 14, wherein a single domain 14 is bounded solely by portions of segment 18 and copy 20 and the rotation 18′ of segment 18, as seen in FIG. 8D. When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 8E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M, C, and V. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_F of the polyhedron chosen times the number of edges P_E per face of the polyhedron, as shown below in Table 8.

TABLE 8
Domains resulting from use of specific polyhedra when using the
Midpoint to Center to Vertex Method

			Number
Type of	Number of Faces,		of Domains
Polyhedron	PF	Number of Edges, PE	14

Tetrahedron	4	3	12
Cube	6	4	24
Octahedron	8	3	24
Dodecahedron	12	5	60
Icosahedron	20	3	60

While the methods described previously provide a framework for the use of center C, vertex V, and midpoint M as the only control points, other control points are useable. For example, a control point may be any point P on an edge E of the chosen polyhedron face. When this type of control point is used, additional types of domains may be generated, though the mechanism for creating the irregular domain(s) may be different. An exemplary method, using a center C and a point P on an edge, for creating one such irregular domain is described below.

The Center to Edge Method

Referring to FIGS. 9A-9E, the center to edge method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

• • 1. A regular polyhedron is chosen (FIGS. 9A-9E use an icosahedron);
  • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 9A;
  • 3. Center C of face 16, and a point P₁ on edge E₁ are connected with a segment 18;
  • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a point P₂ on edge E₂ adjacent to edge E₁, where point P₂ is positioned identically relative to edge E₂ as point P₁ is positioned relative to edge E₁, such that the two segments 18 and 20 and the portions of edges E₁ and E₂ between points P₁ and P₂, respectively, and a vertex V, which connects edges E₁ and E₂, define an element 22, as shown best in FIG. 9B; and
  • 5. Element 22 is rotated about midpoint M₁ of edge E₁ or midpoint M₂ of edge E₂, whichever is located within element 22, as seen in FIGS. 9B-9C, to create a domain 14, as seen in FIG. 9D.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 9E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and P₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_F of the polyhedron chosen times the number of edges P_E per face of the polyhedron divided by 2, as shown below in Table 9.

TABLE 9
Domains resulting from use of specific polyhedra when using the
Center to Edge Method

			Number
Type of	Number of Faces,		of Domains
Polyhedron	PF	Number of Edges, PE	14

Tetrahedron	4	3	6
Cube	6	4	12
Octahedron	8	3	12
Dodecahedron	12	5	30
Icosahedron	20	3	30

Though each of the above described methods has been explained with reference to regular polyhedrons, they may also be used with certain non-regular polyhedrons, such as Archimedean Solids, Catalan Solids, or others. The methods used to derive the irregular domains will generally require some modification in order to account for the non-regular face shapes of the non-regular solids. An exemplary method for use with a Catalan Solid, specifically a rhombic dodecahedron, is described below.

A Vertex to Vertex Method for a Rhombic Dodecahedron

Referring to FIGS. 10A-10E, a vertex to vertex method based on a rhombic dodecahedron yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

• • 1. A single face 16 of the rhombic dodecahedron, as in FIG. 10A;
  • 2. A first vertex V₁ face 16, and a second vertex V₂ adjacent to first vertex V₁ are connected with a segment 18, as shown in FIG. 10B;
  • 3. A first copy 20 of segment 18 is rotated about vertex V₂, such that it connects vertex V₂ to vertex V3 of face 16, a second copy 24 of segment 18 is rotated about center C, such that it connects vertex V₃ and vertex V₄ of face 16, and a third copy 26 of segment 18 is rotated about vertex V₁ such that it connects vertex V₁ to vertex V₄, all as shown in FIG. 10C, to form a domain 14, as shown in FIG. 10D;

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 10E, twelve domains will be used to cover the surface of golf ball 10, one for each face of the rhombic dodecahedron.

One additional embodiment to the above methods of spherical tiling extends these methods to include sub-patterns of dimples within the irregular domain(s) dimple packing 101. The method includes choosing a spherical tiling base geometry and tiling method, defining a sub-pattern of nearest neighbor dimples 102 within the irregular domain(s), and packing dimples within the remaining un-dimpled region. Until the present invention, arranging dimples on the surface of a golf ball has previously been done solely working within a segment of the desired dimple pattern geometry. The present invention is novel because a sub-pattern of nearest neighbor dimples is first defined on the blank spherical segment of the irregular domain(s). The remaining un-dimpled regions are then packed around the initial defining sub-pattern of nearest neighbor dimples. This can yield both aesthetic and aerodynamic performance advantages.

The process is started with a spherical section, which is circumscribed using the vertices of a regular polyhedron (as previously shown in Table 1), and it should be understood that any of the polyhedron types listed in Table 1 can be used. Illustrative examples, shown here consist of a tetrahedron and an icosahedron. Using the mid-point to mid-point tiling method and a tetrahedral base, the irregular domains 101 illustrated in FIG. 11A and FIG. 11B are created.

The dimple sub-pattern can be defined as nearest neighbor dimples on or within edges of one or more of the irregular domains. The sub-pattern 102 in the current example is defined within both irregular domains. Once the sub-pattern is defined, the remaining unpacked spherical region is packed around the initial sub-pattern of dimples as illustrated in FIG. 11C and FIG. 11D, wherein the sub-pattern dimples 102 are denoted by the gray color. Once the sub-pattern is defined and the remaining unpacked spherical region around the initial sub-pattern is packed with dimples, the dimpled spherical region may then be tessellated, as seen in the golf ball 100 shown in FIG. 11E. The sub-pattern dimples may be packed within any number of the irregular domains.

Although the dimple sub-pattern is defined by nearest neighbor dimples, each instance of the sub-pattern may or may not be continuously connected by sub-pattern nearest neighbor dimples around the ball surface after the domains are tessellated.

The method of determining nearest neighbor dimples is illustrated in FIG. 11C, wherein two tangency lines TL are drawn from the center of a first dimple to a potential nearest neighbor dimple. Additionally, a line segment Ls is drawn connecting the center of the first dimple to the center of the potential nearest neighbor dimple. If there is no line segment that is intersected by another dimple, or portion of a dimple, then those dimples are considered to be nearest neighbor dimples.

Additional examples use an icosahedron as the base pattern and the midpoint to midpoint method to create two irregular domains 101 in FIG. 12A. A sub-pattern of dimples 102 are defined within a single domain in, FIG. 12B and FIG. 13A, and additional dimples are defined within the unpacked region of the irregular domains. The irregular domains are tessellated to create a golf ball 100 with a sub-pattern that is connected throughout the tessellation (FIG. 13B) and a golf ball 100 with a sub-pattern that is disconnected throughout the tessellation (FIG. 12C).

Visual distinction may be achieved between the sub-pattern dimples and the remaining dimples, by exhibiting the sub-pattern dimples with one or more of the following characteristics: different perimeter shape; dimple profile; color; texture; grooves; or brambles. Also, the dimples packing the remaining spherical region, which is defined by the existing dimple sub-pattern, may have different perimeter shape, dimple profile, color, or texture.

Dimples with circular perimeters should have diameters that fall within the range of 0.100 to 0.220 inches. Dimples with non-circular perimeters should be circumscribed by a circle with a diameter that falls within the range of 0.120 to 0.270 inches.

Each irregular domain preferably contains between 10 and 115 dimples, and the nearest initial sub-pattern of nearest neighbor dimples preferably contains between 2 and 80 dimples.

Preferred high performance golf balls will usually have a staggered parting line that passes through the section and normally intersects two edges of the section.

The surface coverage of the dimples on the golf ball should be between 70 to 90%, while the surface coverage of the nearest neighbor sub-pattern of dimples should be between 10% and 60%.

Dimples may exhibit a contrasting color(s); the perimeter shape may be circular, polygonal, or elliptical. Dimple profiles can include, but are not limited to, spherical, Gabriel's horn, catenary, conical, Witch of Agnesi, chalice, elliptical, superposition of two curves, or any other spherically weighted profile.

There are no limitations on how the dimples are packed. There are likewise no limitations to the dimple shapes or profiles selected to pack the domains. Though the present invention includes substantially circular dimples in one embodiment, dimples or protrusions (brambles) having any desired characteristics and/or properties may be used. For example, in one embodiment the dimples may have a variety of shapes and sizes including different depths and widths. In particular, the dimples may be concave hemispheres, or they may be triangular, square, hexagonal, catenary, polygonal or any other shape known to those skilled in the art. They may also have straight, curved, or sloped edges or sides. Any type of dimple or protrusion (bramble) known to those skilled in the art may be used with the present invention. Alternatively, the tessellation can create a pattern that covers more than about 60%, preferably more than about 70% and preferably more than about 80% of the golf ball surface.

In other embodiments, the domains may not be packed with dimples, and the borders of the irregular domains may instead comprise ridges or channels. In golf balls having this type of irregular domain, the one or more domains or sets of domains preferably overlap to increase surface coverage of the channels.

When the domain(s) is patterned onto the surface of a golf ball, the arrangement of the domains dictated by their shape and the underlying polyhedron ensures that the resulting golf ball has a high order of symmetry, equaling or exceeding 12. The order of symmetry of a golf ball produced using the method of the current invention will depend on the regular or non-regular polygon on which the irregular domain is based. The order and type of symmetry for golf balls produced based on the five regular polyhedra are listed below in Table 10.

TABLE 10
Symmetry of Golf Ball of the Present Invention
as a Function of Polyhedron

Type of Polyhedron	Type of Symmetry	Symmetrical Order
Tetrahedron	Chiral Tetrahedral Symmetry	12
Cube	Chiral Octahedral Symmetry	24
Octahedron	Chiral Octahedral Symmetry	24
Dodecahedron	Chiral Icosahedral Symmetry	60
Icosahedron	Chiral Icosahedral Symmetry	60

The benefits of these high orders of symmetry include more even dimple distribution, the potential for higher packing efficiency, and improved means to mask the ball parting line. Further, dimple patterns generated in this manner may have improved flight stability and symmetry as a result of the higher degrees of symmetry.

In other embodiments, the irregular domains do not completely cover the surface of the ball, and there are open spaces between domains that may or may not be filled with dimples. This allows dissymmetry to be incorporated into the ball.

In another embodiment, the present invention is directed to dimple patterns based on icosahedral tilings. Isocsahedral tiling is specifically described in U.S. Pat. No. 9,504,877, the entire disclosure of which is hereby incorporated herein by reference in its entirety. The dimple pattern of the present embodiment is arranged in two irregular domains as described in U.S. Pat. No. 9,468,810 and U.S. application Ser. No. 15/263,408, the entire disclosures of which are hereby incorporated herein by reference in their entirety. The preferred icosahedron pattern of the present invention consists of twenty irregular first domains and twelve irregular second domains. Preferably, the first and second irregular domains are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The dimples within the irregular domains consist of a first dimple type that makes up the majority of the dimples on the golf ball and a second dimple type that is different from the first dimple type and constitutes a sub-pattern of nearest neighbor dimples within the irregular domains.

The sub-pattern dimples, or second dimple type, are different in either dimple profile shape and/or in dimple plan shape (i.e. perimeter shape). The sub-pattern of dimples preferably has more than one dimple.

Dimple profiles of either the majority dimples (first dimple type) or the sub-pattern of dimples (second dimple type) may be selected from the group of: spherical dimples, conical dimples as described in U.S. Pat. Nos. 8,137,217, 8,632,426 and 9,220,945 the entire disclosures of which are hereby incorporated herein by reference in their entirety, dimples with rotational protrusions as described in U.S. Pat. No. 8,353,789 the entire disclosure of which is hereby incorporated herein by reference in its entirety, circumscribed prismatoids as described in U.S. Pat. Nos. 8,926,453 and 8,317,638 the entire disclosures of which are hereby incorporated herein by reference in their entirety, frequency dimples or Witch of Agnesi curve dimples as described in U.S. Publ. No. 2012/0122613 the entire disclosure of which is hereby incorporated herein by reference in its entirety, catenary dimples as described in U.S. Pat. Nos. 7,887,439, 7,641,572, 7,163,472 and 6,796,912 the entire disclosures of which are hereby incorporated herein by reference in their entirety, superposition dimples as described in U.S. Publ. Nos. 2016/0279478, 2016/0129314 and 2015/0119171 the entire disclosures of which are hereby incorporated herein by reference in their entirety, Gabriel's horn dimples as described in U.S. Publ. No. 2013/0172124 the entire disclosure of which is hereby incorporated herein by reference in its entirety, and grooved dimples as described in U.S. Publ. No. 2014/0135146 the entire disclosure of which is hereby incorporated herein by reference in its entirety.

Dimple plan shapes of either the majority dimples (first dimple types) or the sub-pattern of dimples (second dimple types) may be selected from one of: circular, polygonal, periodic functions along a path as described in U.S. patent application Ser. Nos. 14/941,841, 14/948,251 and 14/948,252 the entire disclosures of which are hereby incorporated herein by reference in their entirety, circular arcs derived from polygons as described in U.S. patent application Ser. No. 14/941,916 the entire disclosure of which is hereby incorporated herein by reference in its entirety, and irregularly shaped dimples.

For purposes of the embodiments described in FIGS. 14-16 of the present disclosure, each dimple on the outer surface of the golf ball is either a perimeter dimple or an interior dimple and is positioned entirely within either an irregular first domain or an irregular second domain. Perimeter dimples are those dimples located directly adjacent to a border segment. The perimeter dimples of a given irregular domain are those located inside of that domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Interior dimples are those dimples not located directly adjacent to a border segment. The interior dimples of a given irregular domain are those located within the domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Perimeter and interior dimples are described in greater detail in U.S. patent application Ser. No. 15/242,217, the entire disclosure of which is hereby incorporated herein by reference in its entirety.

A specific embodiment is shown in FIGS. 14A-E. This embodiment is a spherical tiling based on an icosahedron pattern having a first domain 200 and a second domain 202. The dimple pattern within each domain is axially symmetric about a center of the domain C₁ and C₂. The first domain 200 and second domain 202 are tessellated to cover the outer surface of the golf ball 208 in a uniform pattern having no great circles and consisting of twenty first domains 200 and twelve second domains 202. The iscosahedron pattern consists of a majority of dimples 204 of a first dimple type and sub-pattern dimples 206 of a second dimple type. As shown in FIGS. 14A-E, the majority of dimples 204 are shown as unshaded while the sub-pattern dimples 206 are identified as the shaded dimples. In this particular example, the majority dimples 204 have a spherical dimple profile as shown in FIG. 14D and a circular plan shape as shown in FIGS. 14A-C, and the sub-pattern dimples 206 have a conical dimple profile as shown in FIG. 14E and a circular plan shape as shown in FIGS. 14A-C. As shown in FIGS. 14A-C, sub-pattern dimples 206 are all perimeter dimples in the first domain 200 and have 3-way axial symmetry about the center C₁ of the first domain 200.

Referring now to the specific embodiment of FIGS. 15A-E, this embodiment is a spherical tiling based on an icosahedron pattern with a first domain 300 and a second domain 302. The dimple pattern within each domain is axially symmetric about a center of the domain C₁ and C₂. The first domain 300 and second domain 302 are tessellated to cover the outer surface of the golf ball 308 in a uniform pattern having no great circles and consisting of twenty first domains 300 and twelve second domains 302. The iscosahedron pattern consists of the majority dimples 304 of a first dimple type and the sub-pattern dimples 306 of a second dimple type. As shown in FIGS. 15A-C, the majority of dimples 304 are shown as unshaded while the sub-pattern dimples 306 are identified as the shaded dimples. In this particular example, the majority dimples 304 have a catenary dimple profile as shown in FIG. 15D and a circular plan shape as shown in FIG. 15A-C, and the sub-pattern dimples 306 have a dimple profile in the shape of a Gabriel's horn as shown in FIG. 15E and a circular plan shape as shown in FIGS. 15A-C. As is apparent from FIGS. 15A-C, the sub-pattern dimples 306 are both perimeter dimples and interior dimples in the second domain 302 and are 5-way axially symmetric about the center C₂ of the second domain 302.

Referring now to the specific embodiment of FIGS. 16A-E, this embodiment is a spherical tiling based on an icosahedron pattern with a first domain 400 and a second domain 402. The dimple pattern within each domain is axially symmetric about the center of the domain C₁ and C₂. The first domain 400 and second domain 402 are tessellated to cover the outer surface of the golf ball 408 in a uniform pattern having no great circles and consisting of twenty first domains 400 and twelve second domains 402. The iscosahedron pattern consists of the majority dimples 404 of a first dimple type and the sub-pattern dimples 406 of a second dimple type. As shown in FIGS. 16A-C, the majority of dimples 404 are shown as unshaded while the sub-pattern dimples 406 are identified as the shaded dimples. In this particular example, the majority dimples 404 have a circular plan shape as shown in FIGS. 16A-D, and the sub-pattern dimples 406 have a discontinuous plan shape using circular arcs as shown in FIGS. 16A-C and E. It is apparent that the sub-pattern dimples 406 are perimeter dimples of the second domain 402 and have five-way axial symmetry about the center C₂ of the second domain 402.

The preferred dimple coverage of the present invention is greater than 75%, or more preferably 80% or more preferably 85%. Preferably, dimple counts for the present invention range from about 200 to about 500 dimples and more preferably from about 300 to about 400 dimples. Preferably, dimples sizes for the present invention range from about 0.10 to about 0.22 inches, more preferably from about 0.12 to about 0.2 inches and most preferably from about 0.125 to about 0.195 inches. As will be appreciated from the drawings, the majority of dimples (first dimple type) and sub-pattern dimples (second dimple type) may include dimples of different sizes.

While the preferred embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not of limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. For example, while the preferred polyhedral shapes have been provided above, other polyhedral shapes could also be used. Thus the present invention should not be limited by the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.