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US 6,309,716 B1Granted
Tessellation set
OwnerAdrian Fisher, Edward Taylor Pegg, Jr.inventors
Life of this patent
Estimating the term…
Abstract
Sets of tessellatable elements are disclosed, in which a relatively low number of different elements may be combined together to provide very attractive tessellating patterns. The elements may be in the form of tiles, for paving or for covering flooring or walls, for example, game pieces, including television and computer games, pieces for use in maze construction and for many other applications.
Claims24
A set of tessellatable elements comprising, at least;
- a four-sided element with internal angles of 60°, 75°, 90° and 135°;
- a five-sided element with internal angles of 60°, 135°, 105°, 105° and 135°;
- and
- a four-sided element with internal angles of 60°, 90°, 90° and 120°.
1 more element
A set of tessellatable elements comprising, at least:
- a five-sided element with internal angles of 60°, 90°, 150°, 30° and 210°;
- and
- a five-sided element with internal angles of 90°, 90°, 150°, 60° and 150°.
A set of tessellatable elements comprising:
- a five-sided element with internal angles of 40°, 200°, 60°, 100° and 140°;
- and
- a five-sided element with internal angles of 80°, 160°, 60°, 140° and 100°.
A set of tessellatable elements comprising:
- a five-sided element with internal angles of 45°, 195°, 60°, 105° and 135°;
- and
- a five-sided element with internal angles of 75°, 165°, 60°, 135° and 105°.
A set of tessellatable elements comprising, at least, any two sets selected from the group of sets comprising:
- (a) at least:
- a four-sided element with internal angles of 60°, 75°, 90° and 135°
- a five-sided element with internal angles of 60°, 135°, 105°, 105° and 135°;
- and
- a four-sided element with internal angles of 60°, 90°, 90° and 120°;
- wherein these elements comprise at least;
- a four sided element with internal angles of 90°, 60°, 75° and 135°, and side lengths of ratio 0.518:1:1:1;
- a five-sided element with internal angles of 60°, 135°, 105°, 105° and 135°, and side lengths of ratio 1:0.518:1:0.518:1;
- and
- a four-sided element with internal angles of 90°, 60°, 120° and 90°, and side lengths of ratio 1:1:1.366:0.355;
- (b) a five-sided element with internal angles of 40°, 200°, 60°, 100° and 140°;
- and
- a five-sided element with internal angles of 80°, 160°, 60°, 140° and 100°;
- wherein these elements comprise at least:
- a five-sided element with internal angles of 40°, 200°, 60°, 100° and 140°, and side lengths of ratio 1:1:1:1:1;
- a five-sided element with internal angles of 80°, 160°, 60°, 140° and 100°, and side lengths of ratio 1:1:1:1:1;
- and
- (c) a five-sided element with internal angles of 45°, 195°, 60°, 105° and 135°;
- and
- a five-sided element with internal angles of 75°, 165°, 60°, 135° and 105°;
- wherein these elements comprise at least a five-sided element of internal angles 45°, 195°, 60°, 105° and 135°, and side lengths of ratio 1:1:1:1:1;
- a five-sided element with internal angles of 75°, 165°, 60°, 135° and 105°, and side lengths of ratio 1:1:1:1:1.
19 more elements
A set of tessellatable elements comprising, at least, two of the elements selected from the group comprising:
- No. Sides Ratio Internal Angles 4 1:1:1:1 90°, 90°, 90°, 90° 4 four of 0.518 90°, 90°, 90°, 90° 4 0.518:1:1:1 90°, 60°, 75°, 135° 4 1:1:1:1 60°, 120°, 60°, 120° 5 1:0.518:1:0.518:1 60°, 135°, 105°, 105°, 135° 4 1:1:1.366:0.355 90°, 60°, 120°, 90° 4 1:1:1:0.482 105°, 105°, 75°, 75° 5 1:1:three of 0.518 90°, 75°, 150°, 150°, 75° 6 six of 0.518 90°, 120°, 90°, 120°, 90°, 120° 12 twelve of 1 270° and 30° alternately 5 1:1:1:1:1 60°, 90°, 150°, 30°, 210° 5 1:1:1:1:1 90°, 90°, 150°, 60°, 150° 3 1:2:1.732 90°, 60°, 30° 4 1:1:1:1 150°, 30°, 150°, 30° 5 1:1:1:1:1 40°, 200°, 60°, 100°, 140° 5 1:1:1:1:1 80°, 160°, 60°, 140°, 100° 4 1:1:1:0.347 60°, 80°, 80°, 140° 4 1:1:1:1 100°, 80°, 100°, 80° 4 1:1:1:1 140°, 40°, 140°, 40° 12 twelve of 1 260° and 40° alternately 5 1:1:1:1:1 45°, 195°, 60°, 105°, 135° 5 1:1:1:1:1 75°, 165°, 60°, 135°, 105° 4 1:1:1:0.261 60°, 75°, 82.5°, 142.5° 4 1:1:1:1 135°, 45°, 135°, 45° 12 twelve of 1 255° and 45° alternately 6 1:1:1:1:1:1 270°, 60°, 90°, 150°, 90°, 60° 6 1:1:1:1:1:1 90°, 60°, 210°, 90°, 60°, 120° 6 1:1:1:1:1:1 60°, 150°, 60°, 210°, 30°, 210°
A set of tessellatable elements comprising at least one of the following:
- (a) pieces of a Mitre Set, a 12-gon Set, an 18-gon Set and a 24-gon Set;
- (b) pieces of the Mitre set arranged in an adjacent relationship to form a plurality of nested squares of different sizes;
- (c) pieces of the Mitre Set arranged to form tiling patterns that have 2, 3, 4, 6 and 12 axes of symmetry;
- (d) pieces of the 12-gon and 18-gon Sets arranged to share the same topology;
- (e) pieces of the 12-gon Set arranged to fill a plurality of 12-sided regular polygons of different sizes;
- (f) pieces of the 12-gon Set arranged to form tiling patterns that have 2, 3, 4, 6 and 12 axes of symmetry;
- (g) pieces of the 18-gon Set arranged to form aperiodic tiling patterns;
- (h) pieces of the 18-gon Set arranged to fill a plurality of 18-sided regular polygons of different sizes;
- (i) pieces of the 18-gon Set arranged to form periodic tiling patterns that have 3, 6, 9 and 18 axes of symmetry;
- (j) pieces of the 12-gon set and the 24-gon set arranged to share the same topology;
- (k) pieces of the 24-gon Set that arranged to form tilings that fill a plurality of 24-sided regular polygons of different sizes;
- and
- (l) pieces of the 24-gon Set arranged to form periodic tiling patterns that have 2, 3, 4, 6, 12 and 24 axes of symmetry.
10 more elements
Dependencies are inferred from the claim text.