Tessellation set

Details Tessellation set Tessellation set

1999-09-24

2001-10-30

Jones, Deborah (Department: 1775)

Stock material or miscellaneous articles

Plural parts with edges or temporary joining means each...

C428S015000, C428S044000, C428S042100, C428S054000, C428S055000, C428S542200, C428S542800, C434S081000, C434S096000, C434S211000, C273S15700R, C273S293000, C052S311100, C052S311200

Reexamination Certificate

active

06309716

ABSTRACT:

BACKGROUND OF THE INVENTION
This invention relates generally to tessellatable elements and more specifically, but not exclusively, to tessellations for covering surfaces.
The covering of surfaces such as floors, walls and ceilings with decorative patterns is well known. Often, floor surfaces are covered with bricks, paving stones or other such similar media. One way decorative patterns can be made is to periodically repeat shapes to build-up a mosaic-like covering. These types of patterns will often have an inherent symmetry; translational, rotational, etc.
Decorative patterns can be realised using such tessellatable elements as are disclosed in U.S. Pat. No. 5,945,181. Here, heptagonal and pentagonal elements are tessellated to produce patterns and/or decorations suitable for covering floor or walls.
Certain surface spaces cannot be tiled totally with heptagonal and/or pentagonal tiles only, since gaps will result if rectangular spaces are tiled with such elements. The only remedy to this problem would be to cut the tiles to achieve ‘wall-to-wall’ coverage. The aesthetic nature of designs made with such tiles is also limited.
The present invention arose in an attempt to provide a set of elements capable of tessellating a surface which is delimited by straight perimeter edges or otherwise, without having to pre-cut any of the elements.
It was also desirable to minimise the number of different shaped elements within a given set, and also to devise sets whose elements could be interchanged.
A further object of the invention is to provide a set of elements which can be tessellated in many different ways, to produce very attractive patterns.
BRIEF SUMMARY OF THE INVENTION
According to a first aspect of the present invention there is provided a set of tessellatable elements comprising:
a four-sided element with internal angles of 60°, 75°, 90° and 135°;
a five-sided element with internal angles of 60°, 105°, 105°, 135° and 135°; and
a four-sided element with internal angles of 60°, 90°, 90° and 120°.
According to a second aspect of the present invention there is provided a set of tessellatable elements comprising:
a five-sided element with internal angles of 30°, 60°, 90°, 150° and 210°; and
a five-sided element with internal angles of 60°, 90°, 90°, 150° and 150°.
According to a third aspect of the present invention there is provided a set of tessellatable elements comprising:
a five-sided element with internal angles of 40°, 60°, 100°, 140° and 200°; and
a five-sided element with internal angles of 60°, 80°, 100°, 140° and 160°.
According to a fourth aspect of the present invention there is provided a set of tessellatable elements comprising:
a five-sided element with internal angles of 45°, 60°, 105°, 135° and 195°; and
a five-sided element with internal angles of 60°, 75°, 105°, 135° and 165°.
The elements are preferably tiles, bricks or paving slabs for covering or decorating wall or floor surfaces without the need for cutting or trimming the elements.
In a further aspect, the present invention provides a set of tessellatable elements comprising any two or more of any individual elements forming part of any of the sets according to any of the first to fourth aspects of the invention.
In a further aspect, the present invention provides a set of tessellatable elements comprising any two or more of the elements hereinafter described and shown.
In accordance with other aspects of the invention, pieces or elements of the various sets (Mitre, 12-gon, 18-gon, 24-gon) can be used with the same set or in another or other sets to form geometric figures (e.g., squares, hexagons and triangles), periodic tiling patterns and aperiodic tiling patterns, sequences of geometric and polygonal figures (e.g., squares, hexagons, etc. of increasing size and/or with nested figures), tilings which share the same topology, and tilings with various axes of symmetry.


REFERENCES:
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patent: 5697520 (1997-12-01), Gerber
patent: 5945181 (1999-08-01), Fisher
patent: 42 43 584 A1 (1994-05-01), None
patent: 0 487 807 (1992-06-01), None
patent: 1 759 943 (1998-08-01), None

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