Space structures with non-periodic subdivisions of polygonal faces
First Claim
1. Curved space structures comprising:
- a polygonal structure having p sides, where p is an integer greater than two, whereinsaid structure is composed of a plurality of 4-sided and 3-sided polygonal elements, each said element having vertices and edges, and arranged side by side such that two adjacent said elements share one of said edges and said 3-sided polygonal elements lie on the peripheri of said plurality of said 4-sided elements and share said edges with said sides of said polygonal structuresaid elements are further arranged such that at least two said vertices of each adjacent said element lie on a continuous curved surface,said elements, said edges and said vertices are engaged with one another by attachment means, andwhere the arrangement of said elements is identical to the arrangement of a plurality of at least two different sets of identical parallelograms and half-parallelograms in a corresponding plane regular polygon with p equal sides and p equal angles such that every said 4-sided element in said curved polygonal structure corresponds to a said parallelogram in said plane polygon and every said 3-sided element in said polygonal structure corresponds to a said half-parallelogram in said plane polygon, wherein said half-parallelograms are obtained by bisecting said parallelograms, whereinsaid arrangement of said parallelograms within at least one said polygonal structure includes at least a portion which is non-periodic, and further includes a cluster of more than four said elements around at least two said vertices, whereinthe interior angles of said parallelograms of said sets equal 180°
/n multiplied by `a`, where `a` equals all integers ranging from 1 to n-1, and n equals p, 2p or p/2.
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Abstract
A family of space structures having subdivided faces, where such faces are subdivided into rhombii in non-periodic arrangements. The rhombii are derived from regular planar stars with n vectors, and the source space structures are composed of regular polygons. The family includes: globally symmetric structures where the fundamental region is subdivided non-periodically, or globally asymmetric structures composed of regular polygons which are subdivided non-periodically or asymmetrically. The rhombii can be further subdivided periodically or non-periodically. The family further includes all regular polyhedra in the plane-faced and curve-faced states, regular tessellations, various curved polygons, cylinders and toroids, curved space labyrinths, and regular structures in higher-dimensional and hyperbolic space. The structures can be isolated structures or grouped to fill space. Applications include architectural space structures, fixed or retractable space frames, domes, vaults, saddle structures, plane or curved tiles, model-kits, toys, games, and artistic and sculptural works realized in 2- and 3-dimensions. The structures could be composed of individual units capable of being assembled or disassembled, or structures which are cast in one piece, or combination of both. Various tensile and compressive structural systems, and techniques of triangulation could be used as needed for stability.
142 Citations
25 Claims
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1. Curved space structures comprising:
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a polygonal structure having p sides, where p is an integer greater than two, wherein said structure is composed of a plurality of 4-sided and 3-sided polygonal elements, each said element having vertices and edges, and arranged side by side such that two adjacent said elements share one of said edges and said 3-sided polygonal elements lie on the peripheri of said plurality of said 4-sided elements and share said edges with said sides of said polygonal structure said elements are further arranged such that at least two said vertices of each adjacent said element lie on a continuous curved surface, said elements, said edges and said vertices are engaged with one another by attachment means, and where the arrangement of said elements is identical to the arrangement of a plurality of at least two different sets of identical parallelograms and half-parallelograms in a corresponding plane regular polygon with p equal sides and p equal angles such that every said 4-sided element in said curved polygonal structure corresponds to a said parallelogram in said plane polygon and every said 3-sided element in said polygonal structure corresponds to a said half-parallelogram in said plane polygon, wherein said half-parallelograms are obtained by bisecting said parallelograms, wherein said arrangement of said parallelograms within at least one said polygonal structure includes at least a portion which is non-periodic, and further includes a cluster of more than four said elements around at least two said vertices, wherein the interior angles of said parallelograms of said sets equal 180°
/n multiplied by `a`, where `a` equals all integers ranging from 1 to n-1, and n equals p, 2p or p/2. - View Dependent Claims (5, 6, 11, 12, 14, 15, 16, 17)
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2. Curved space structures comprising:
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a plurality of curved polygonal structures, each having p sides, where p is an integer greater than two, and wherein at least two said polygonal structures meet at each said side, wherein each said polygonal structure is composed of a plurality of 4-sided and 3-sided polygonal elements, each said element having vertices and edges, and arranged side by side such that two adjacent said elements share one of said edges and said 3-sided polygonal elements lie on the peripheri of said plurality of said 4-sided elements and share said edges with said sides of said polygonal structure said elements are further arranged such that at least two said vertices of each adjacent said element lie on a continuous curved surface, said elements, said edges and said vertices are engaged with one another by attachment means, and where the plurality of said curved polygonal structures corresponds to a plurality of plane regular polygons, each with p equal sides and p equal angles, and where the arrangement of said elements within each said polygonal structure is identical to the arrangement of a plurality of at least two different sets of identical parallelograms and half-parallelograms in corresponding said plane regular polygon such that every said 4-sided element in each said curved polygonal structure corresponds to a said parallelogram in corresponding said plane regular polygon and every said 3-sided element in said polygonal structure corresponds to a said half-parallelogram in said plane polygon, wherein said half-parallelograms are obtained by bisecting said parallelograms, wherein said arrangement of said parallelograms within at least one said polygonal structure includes at least a portion which is non-periodic, and further includes a cluster of more than four said elements around at least two said vertices, wherein the interior angles of said parallelograms of said sets equal 180°
/n multiplied by `a`, where `a` equals all integers ranging from 1 to n-1, and n equals p, 2p or p/2. - View Dependent Claims (7, 8, 13, 18, 19, 20, 21, 22, 23, 24, 25)
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3. Space structures comprising:
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a plurality of plane polygonal structures, each having p sides and p angles, wherein at least two said polygonal structures meet at each said side and where p is an integer greater than two, wherein each said polygonal structure is composed of a plurality of at least two different sets of identical 4-sided and 3-sided polygonal elements, each said element having vertices and edges, and arranged side by side such that two adjacent said elements share one of said edges and said 3-sided polygonal elements lie on the peripheri of said plurality of said 4-sided elements and share said edges with said sides of said polygonal structure wherein said 4-sided elements are parallelograms and said 3-sided elements are half-parallelograms and where said half-parallelograms are obtained by bisecting said parallelograms, said elements are further arranged within said polygonal structure such that said vertices and said edges of each adjacent said element lie on a continuous plane surface, said elements, said edges and said vertices are engaged with one another by attachment means, and said arrangement of said parallelograms within at least one said polygonal structure includes at least a portion which is non-periodic, and further includes a cluster of more than four said elements around at least two said vertices, wherein the interior angles of said parallelograms of said sets equal 180°
/n multiplied by `a`, where `a` equals all integers ranging from 1 to n-1, and n equals p, 2p or p/2. - View Dependent Claims (4, 9, 10)
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Specification