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US 4,723,382 AGranted
Building structures based on polygonal members and icosahedral
OwnerHaresh Lalvaniinventor
Life of this patent
Estimating the term…
Abstract
Building structures based on polygonal members with coplanar straight edges and icosahedral symmetry. The building structures comprise a set of ten elementary polygonal members, including four triangular members and six parallelogram-shaped members, that are combined to form tetrahedral, octahedral and half-octahedral or trucated tetrahedral, cuboctahedral and truncated octahedral or rhombohedral and parallelpiped building members that in turn fill a three-dimensional space periodically or non-periodically. The orientation of the building members is such that all edges are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry.
Claims8
A set of polygonal members for constructing a building structure and being combinable to form a set of polyhedral members that, when placed adjacent one another, continuously fill three-dimensional space periodically or non-periodically, the combination comprising:
- ten elementary polygonal members, which have coplanar straight edges, including where .phi. is 1.61803,
- a first triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x,
- a second triangular member, which is isosceles, has two base angles of 36.degree. and an apex angle of 108.degree., and has two edges of a length x and a base of x.phi.,
- a third triangular member, which is isosceles, has two base angles of 72.degree. and an apex angle of 36.degree., and has two edges of a length x.phi. and a base of x,
- a fourth triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x.phi.,
- a first parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x,
- a second parallelogram-shaped member, which is a rectangle, has four interior angles of 90.degree. each, and has two equal edges of a length x and two other equal edges of a length x.phi.,
- a third parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x.phi.,
- a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36.degree. and two other interior angles of 144.degree., and has four equal edges of a length x,
- a fifth parallelogram-shaped member, which has two interior angles of 60.degree. and two other interior angles of 120.degree., and has two equal edges of a length x and two other equal edges of a length x.phi., and a sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72.degree. and two other interior angles of 108.degree., and has four equal edges of a length x.phi.,
- said ten elementary polygonal members being combinable to produce six complementary pairs of polyhedral three-dimensional building members,
- the orientation of said polyhedral building members, when placed adjacent one another, being such that all edges of said building members are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry,
- said building members being capable of filling three-dimensional space periodically or non-periodically.
10 more elements
A set of polygonal members for constructing a building structure and being combinable to form a set of polyhedral members that, when placed adjacent one another continuously, fill three-dimensional space periodically or non-periodically, the combination comprising:
- ten elementary polygonal members, which have coplanar straight edges, including where .phi. is 1.61803,
- a first triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x,
- a second triangular member, which is isosceles, has two base angles of 36.degree. and an apex angle of 108.degree., and has two edges of a length x and a base of x.phi.,
- a third triangular member, which is isosccles, has two base angles of 72.degree. and an apex angle of 36.degree., and has two edges of a length x.phi. and a base of x,
- a fourth triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x.phi.,
- a first parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x,
- a second parallelogram-shaped member, which is a rectangle, has four interior angles of 90.degree. each, and has two equal edges of a length x and two other equal edges of a length x.phi.,
- a third parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x.phi.,
- a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36.degree. and two other interior angles of 144.degree., and has four equal edges of a length x,
- a fifth parallelogram-shaped member, which has two interior angles of 60.degree. and two other interior angles of 120.degree., and has two equal edges of a length X and two other equal edges of a length x.phi., and
- a sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72.degree. and two other interior angles of 108.degree., and has four equal edges of a length x.phi., and
- four hexagonal members including
- a first hexagonal member formed of six of said first triangular members,
- a second hexagonal member formed of six of said second triangular members,
- a third hexagonal member formed of six of said third triangular members, and
- a fourth hexagonal member formed of six of said fourth triangular members,
- said ten elementary polygonal members and said four hexagonal members being combinable to produce six sets of polyhedral three-dimensional building members,
- said pairs each comprising a truncated tetrahedral member and either a cuboctahedral member or a truncated octahedral member,
- the orientation of said polyhedral building members, when placed adjacent one another, being such that all edges of said building members are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry,
- said building members being capable of filling three-dimensional space periodically or non-periodically.
17 more elements
A set of polygonal members for constructing a building structure and being combinable to form a set of polyhedral members that, when placed adjacent one another continuously fill three-dimensional space periodically or non-periodically, the combination comprising:
- ten elementary polygonal members, which have coplanar straight edges, including where .phi. is 1.61803,
- a first triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x,
- a second triangular member, which is isosceles, has two base angles of 36.degree. and an apex angle of 108.degree., and has two edges of a length x and a base of x.phi.,
- a third triangular member, which is isosceles, has two base angles of 72.degree. and an apex angle of 36.degree., and has two edges of a length x.phi. and a base of x,
- a fourth triangular member, which is equilateral, has three interior angles of 60.degree. each, and has three equal edges of a length x.phi.,
- a first parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x,
- a second parallelogram-shaped member, which is a rectangle, has four interior angles of 90.degree. each, and has two equal edges of a length x and two other equal edges of a length x.phi.,
- a third parallelogram-shaped member, which is square, has four interior angles of 90.degree. each, and has four equal edges of a length x.phi.,
- a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36.degree. and two other interior angles of 144.degree., and has four equal edges of a length x,
- a fifth parallelogram-shaped member, which has two interior angles of 60.degree. and two other interior angles of 120.degree., and has two equal edges of a length x and two other equal edges of a length x.phi. and
- a sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72.degree. and two other interior angles of 108.degree., and has four equal edges of a length x.phi.,
- said ten elementary polygonal members being combinable to produce polyhedral three-dimensional building members,
- the orientation of said polyhedral building members, when placed adjacent one another, being such that all edges of said building members are parallel to the fifteen two-fold axes of rotation of icosahedral symmetry,
- said building members being capable of filling three-dimensional space periodically or non-periodically.
11 more elements
Dependencies are inferred from the claim text.