Irregular, rotational tessellation surface covering units and surface covering
A surface covering unit comprises x primary elements, wherein x is an integer equal to or greater than 1. Each primary element is a rotational tessellation having a plural pairs of sides extending in a generally radial direction from plural vertices, respectively. In each pair, the two sides are rotationally spaced by an angle of 60, 90, 120 or 180 degrees, and each side is substantially a rotational image of the other side. The sum of the plural vertices angles is 180, 240, 270, 300 or 360 degrees. Preferably, all of the sides are irregularly shaped, but one or more sides could be wholly or partially straight. Optionally, one or more edges of each unit are marked with indicia to facilitate matching mating sides of adjacent units. A wide variety of units may be constructed having different numbers and arrangements of primary elements. As all the units are combinations of primary elements, they readily mate with each other. A surface covering comprises a multiplicity of surface covering units assembled to form a continuous surface without overlap between units and without substantial gaps between units. Because of the irregular side configurations, and different sizes and shapes of individual units, one can construct a continuous surface that has a natural, random and apparent custom appearance. Optionally, minor surface and edges variations are made from unit to unit to further enhance the natural appearance of the surface covering.
1. A surface covering unit comprised of x primary elements, wherein x is an integer equal to or greater than 2, each primary element being a rotational tessellation having
a first side extending in a generally radial direction relative to a first vertex, said first side being irregularly shaped;
a second side extending in a generally radial direction relative to the first vertex and being rotationally spaced from said first side by a first angle of 60, 90, 120 or 180 degrees, said second side being substantially a rotational image of said first side;
a third side extending in a generally radial direction relative to a second vertex, the second vertex being spaced from the first vertex, and
a fourth side extending in a generally radial direction relative to the second vertex and being substantially a rotational image of said third side and rotationally spaced therefrom by a second angle, wherein the sum of the first and second angles is 180, 240, 270 or 300 degrees.
2. A surface covering unit as in claim 1 , wherein the first and second angles are equal.
3. A surface covering unit as in claim 1 , wherein the first and second angles are not equal.
4. A surface covering unit as in claim 1 , comprising at least three of said primary elements, at least two of said elements sharing a common first vertex and at least two of said elements sharing a common second vertex.
5. A surface covering unit as in claim 1 , wherein said primary element further comprises a fifth side and a sixth side extending in a generally radial direction relative to a third vertex, said sixth side being substantially a rotational image of said fifth side, said fifth and sixth sides being rotationally spaced by a third angle, and where in the sum of the first, second and third angles is 360 degrees.
6. A surface covering unit as in claim 1 , wherein said first side bears an indicia spaced a distance from the first vertex, and said second side bears a corresponding indicia spaced substantially the same distance from the first vertex.
7. A surface covering unit as in claim 1 , wherein said first side bears a first indicia and said second side bears a corresponding indicia; and said third side bears a second indicia and said fourth side bears a corresponding indicia to said second indicia.
8. A surface covering unit, comprising
a first side extending in a generally radial direction relative to a first vertex, said first side being irregularly shaped;
a second side extending in a generally radial direction relative to the first vertex and being rotationally spaced from said first side by a first angle of 60, 90, 120, or 180 degrees, said second side being substantially a rotational image of said first side;
a third side extending in a generally radial direction relative to a second vertex, the second vertex being spaced from the first vertex;
a fourth side extending in a generally radial direction relative to the second vertex, said fourth side being substantially a rotational image of said third side, said third and fourth sides being rotationally spaced by a second angle;
the sum of the first and second angles is 180, 240, 270 or 300 degrees, and
wherein the first and second angles are not equal.
9. A surface covering unit as in claim 8 , wherein the first angle is 60 degrees and the second angle is 180 degrees.
10. A surface covering unit as in claim 8 , wherein the first angle is 60 degrees and the second angle is 120 degrees.
11. A surface covering unit as in claim 8 , wherein the first angle is 90 degrees and the second angle is 180 degrees.
12. A collection of surface covering units, each unit comprised of x primary elements, where x is an integer equal to or greater than 1, and each said primary element being a rotational tessellation comprising
a first side extending in a generally radial direction relative to a first vertex, said first side being irregularly shaped;
a second side extending in a generally radial direction relative to said first vertex and being rotationally spaced from said first side by a first angle of 60, 90, 120 or 180 degrees, said second side being substantially a rotational image of said first side;
a third side extending in a generally radial direction from a second vertex, said third side being irregularly shaped, said second vertex spaced apart from said first vertex;
a fourth side extending in a generally radial direction from said second vertex, said fourth side being substantially a rotational image of said third side, said fourth side being rotationally spaced from said third side by a second angle, the sum of the first and second angles being 180, 240, 270 or 300 degrees; and
indicia on at least two sides of each said unit to facilitate matching adjacent units.
13. A collection of surface covering units as in claim 12 comprising a plurality of first units, each first unit comprised of at least one primary element; and a plurality of second units, each second unit comprised of at least two primary elements.
14. A collection of surface covering units as in claim 13 further comprising a plurality of third units, each said third unit comprised of at least three primary elements.
15. A collection of surface covering units as in claim 14 where in said at least three primary elements do not all share one common vertex.
16. A collection of surface covering units as in claim 12 , wherein each said unit carries a first pair of said indicia and a different second pair of said indicia.
17. A surface covering formed of irregular units, comprising
a multiplicity of first units and a multiplicity of second units assembled to form a continuous surface without overlap between units and without substantial gaps between units;
each said unit comprised of x primary elements, where x is an integer equal to or greater than 1, said first units comprising at least one primary element and said second units comprising at least two primary elements, the planar shape of said second units being different from said first units; and
said primary element being a rotational tessellation having
a first side extending in a generally radial direction relative to a first vertex, said first side being irregularly shaped;
a second side extending in a generally radial direction relative to the first vertex and being rotationally spaced from said first side by a first angle of 60, 90, 120 or 180 degrees, said second side being substantially a rotational image of said first side;
a third side extending in a generally radial direction from a second vertex, said third side being irregularly shaped, said second vertex spaced apart from said first vertex; and
a fourth side extending in a generally radial direction from the second vertex, said fourth side being substantially a rotational image of said third side, said fourth side being rotationally spaced from said third side by a second angle, the sum of the first and second angles being 180, 240, 270 or 300 degrees.
18. A surface covering as in claim 17 comprising a multiplicity of third units, each said third unit formed of at least two primary elements and having a planar shape different from both said first units and said second units.
19. A surface covering as in claim 17 wherein some of said units have surface variations different for other ones of said units.
20. A surface covering as in claim 17 wherein some of said units have color variations different from other ones of said units.
21. A surface covering as in claim 17 wherein some of said units have edge variations different from other ones of said units.