Single Aperiodic Shaped Tile

Description

PRIOR ART

• • U.S. Pat. No. 10,190,322 INTERLOCKING ARCH TILE
  • U.S. Pat. No. 10,995,498B1 Polygon tile for tessellating and method of making the same

BACKGROUND OF THE INVENTION

Traditional commercial and residential tiling for flooring and countertops typically form repeating patterns leading to predictable and less visually appealing designs. This invention addresses the need for a tile that provides a unique, non-repeating pattern, enhancing the aesthetic appeal of residential and commercial spaces.

SUMMARY OF THE INVENTION

The present invention relates to a tile with a unique Single Aperiodic Shape, also known as an Einstein Tile. This shape allows a single to cover larger surface than itself without forming repeating patterns. The tiles can be made from various materials, including ceramics, stone, synthetics and fabrics making it versatile for different applications and environments.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1: Is a Top view of the Hat (105) tile.

FIG. 2: An example layout of Hat tiles (105).

FIG. 3: Is a perspective view of the Hat (105) tile.

FIG. 4: Is a Top view of an embodiment of a Single Aperiodic Shape named Turtle (106) showing its 14 vertices (101 & 102) and its 14 sides (103 & 104).

FIG. 5: An example layout of a multitude of Turtle tiles (106) showing a non-repeating pattern.

FIG. 6: Is a perspective view of the Turtle (106) aperiodic shaped tile.

FIG. 7: Is a Top view of an embodiment of a Single Aperiodic Shape named Spectre (107) showing its 14 vertices (101 & 102) and its 14 sides (103 & 104).

FIG. 8: An example layout of a multitude of Spectre tiles (107) showing a non-repeating pattern.

FIG. 9: Is a perspective view of the Spectre (107) aperiodic shaped tile.

DETAILED DESCRIPTION OF THE INVENTION

The published paper ‘A Chiral Aperiodic Monotile’ (2023) by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss confirmed the existence of these once theoretical shapes that can completely tile an infinite surface with a single shape without any repeating patterns. These shapes are called Aperiodic Monotiles or colloquially an Einstein tile. The present invention leverages these mathematical principles to create uniquely shaped tiles for an exclusive high-end look.

The primary function of the present invention is to be used in household or commercial applications. Unlike other tiles that create a predictable and repeating pattern, these tiles ensure that the layout is always unique. This differentiation is particularly appealing for interior designers and architects seeking to create one-of-a-kind spaces.

The tiles themselves can be made from various materials such as ceramics, stone, concrete, plastics, synthetics or fabrics allowing for versatility in its application. The aperiodic nature allows for endless design possibilities, making each installation unique.

FIG. 1 illustrates an embodiment of a tile with an aperiodic shape, commonly called Hat (105). This shape is a polygon with 14 unit-length edges (103 & 104) and 14 vertices (101 & 102), with one vertex (102) located between two collinear edges (104).

FIG. 2 illustrates an example layout of a multitude of Hat tiles (105) demonstrating that a single tile can cover an entire surface without a repeating pattern.

FIG. 3 illustrates a perspective view of the Hat tile (105) which includes a top surface (200), a bottom surface (201), and marginal faces (202) along the polygon perimeter (203). The top surface (200) is designed for exterior exposure, while the bottom surface (201) contacts a sub-surface. The polygon perimeter (203) forms a Single Aperiodic Shape. The marginal faces (202) extend around the perimeter (203) and are generally perpendicular to the top surface (200).

FIG. 4 illustrates an embodiment of a tile with an aperiodic shape, commonly called Turtle (106). This shape is a polygon with 14 unit-length edges (103 & 104) and 14 vertices (101 & 102), with one vertex (102) located between two collinear edges (104).

FIG. 5 illustrates an example layout of a multitude of Turtle tiles (106) demonstrating that a single tile can cover an entire surface without a repeating pattern.

FIG. 6 illustrates a perspective view of the Turtle tile (106) which includes a top surface (200), a bottom surface (201), and marginal faces (202) along the polygon perimeter (203). The top surface (200) is designed for exterior exposure, while the bottom surface (201) contacts a sub-surface. The polygon perimeter (203) forms a Single Aperiodic Shape. The marginal faces (202) extend around the perimeter (203) and are generally perpendicular to the top surface (200).

FIG. 7 illustrates an embodiment of a tile with an aperiodic shape, commonly called Spectre (107). This shape is a polygon with 14 unit-length edges (103 & 104) and 14 vertices (101 & 102), with one vertex (102) located between two collinear edges (104).

FIG. 8 illustrates an example layout of a multitude of Spectre tiles (107) demonstrating that a single tile can cover an entire surface without a repeating pattern.

FIG. 9 illustrates a perspective view of the Spectre tile (107) which includes a top surface (200), a bottom surface (201), and marginal faces (202) along the polygon perimeter (203). The top surface (200) is designed for exterior exposure, while the bottom surface (201) contacts a sub-surface. The polygon perimeter (203) forms a Single Aperiodic Shape. The marginal faces (202) extend around the perimeter (203) and are generally perpendicular to the top surface (200).

Many different tile shapes of the various components depicted, as well as components not shown, are possible without departing from the spirit and scope of the present disclosure. Embodiments of the present disclosure have been described with the intent to be illustrative rather than restrictive. Alternative embodiments will become apparent to those skilled in the art that do not depart from its scope. A skilled artisan may develop alternative means of implementing the aforementioned improvements without departing from the scope of the present disclosure.

It will be understood that certain features and sub combinations are of utility and may be employed without reference to other features and sub combinations and are contemplated within the scope of the claims. Not all steps listed in the various figures need be carried out in the specific order described.