Building structures based on polygonal members and icosahedral
First Claim
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1. 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 φ
is 1.61803,a first triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length x,a second triangular member, which is isosceles, has two base angles of 36° and
an apex angle of 108°
, and has two edges of a length x and a base of xφ
,a third triangular member, which is isosceles, has two base angles of 72° and
an apex angle of 36°
, and has two edges of a length xφ and
a base of x,a fourth triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length xφ
,a first parallelogram-shaped member, which is square, has four interior angles of 90°
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°
each, and has two equal edges of a length x and two other equal edges of a length xφ
,a third parallelogram-shaped member, which is square, has four interior angles of 90°
each, and has four equal edges of a length xφ
,a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36° and
two other interior angles of 144°
, and has four equal edges of a length x,a fifth parallelogram-shaped member, which has two interior angles of 60° and
two other interior angles of 120°
, and has two equal edges of a length x and two other equal edges of a length xφ
, and a sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72° and
two other interior angles of 108°
, and has four equal edges of a length xφ
,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.
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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.
101 Citations
8 Claims
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1. 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:
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ten elementary polygonal members, which have coplanar straight edges, including where φ
is 1.61803,a first triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length x,a second triangular member, which is isosceles, has two base angles of 36° and
an apex angle of 108°
, and has two edges of a length x and a base of xφ
,a third triangular member, which is isosceles, has two base angles of 72° and
an apex angle of 36°
, and has two edges of a length xφ and
a base of x,a fourth triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length xφ
,a first parallelogram-shaped member, which is square, has four interior angles of 90°
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°
each, and has two equal edges of a length x and two other equal edges of a length xφ
,a third parallelogram-shaped member, which is square, has four interior angles of 90°
each, and has four equal edges of a length xφ
,a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36° and
two other interior angles of 144°
, and has four equal edges of a length x,a fifth parallelogram-shaped member, which has two interior angles of 60° and
two other interior angles of 120°
, and has two equal edges of a length x and two other equal edges of a length xφ
, and a sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72° and
two other interior angles of 108°
, and has four equal edges of a length xφ
,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. - View Dependent Claims (2, 3, 4)
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5. 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:
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ten elementary polygonal members, which have coplanar straight edges, including where φ
is 1.61803,a first triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length x,a second triangular member, which is isosceles, has two base angles of 36° and
an apex angle of 108°
, and has two edges of a length x and a base of xφ
,a third triangular member, which is isosccles, has two base angles of 72° and
an apex angle of 36°
, and has two edges of a length xφ and
a base of x,a fourth triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length xφ
,a first parallelogram-shaped member, which is square, has four interior angles of 90°
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°
each, and has two equal edges of a length x and two other equal edges of a length xφ
,a third parallelogram-shaped member, which is square, has four interior angles of 90°
each, and has four equal edges of a length xφ
,a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36° and
two other interior angles of 144°
, and has four equal edges of a length x,a fifth parallelogram-shaped member, which has two interior angles of 60° and
two other interior angles of 120°
, and has two equal edges of a length X and two other equal edges of a length xφ
, anda sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72° and
two other interior angles of 108°
, and has four equal edges of a length xφ
, andfour 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.
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6. 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 φ
is 1.61803,a first triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length x,a second triangular member, which is isosceles, has two base angles of 36° and
an apex angle of 108°
, and has two edges of a length x and a base of xφ
,a third triangular member, which is isosceles, has two base angles of 72° and
an apex angle of 36°
, and has two edges of a length xφ and
a base of x,a fourth triangular member, which is equilateral, has three interior angles of 60°
each, and has three equal edges of a length xφ
,a first parallelogram-shaped member, which is square, has four interior angles of 90°
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°
each, and has two equal edges of a length x and two other equal edges of a length xφ
,a third parallelogram-shaped member, which is square, has four interior angles of 90°
each, and has four equal edges of a length xφ
,a fourth parallelogram-shaped member, which is a rhombus, has two interior angles of 36° and
two other interior angles of 144°
, and has four equal edges of a length x,a fifth parallelogram-shaped member, which has two interior angles of 60° and
two other interior angles of 120°
, and has two equal edges of a length x and two other equal edges of a length xφ anda sixth parallelogram-shaped member, which is a rhombus, has two interior angles of 72° and
two other interior angles of 108°
, and has four equal edges of a length xφ
,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. - View Dependent Claims (7, 8)
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Specification
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Current AssigneeHaresh Lalvani
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Original AssigneeHaresh Lalvani
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InventorsLalvani, Haresh
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Primary Examiner(s)Raduazo, Henry E.
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Application NumberUS06/896,848Time in Patent Office543 DaysField of Search52/DIG. 10, 52/81, 52/648, 52/79.4, 434/403, 273/157 RUS Class Current52/81.1CPC Class CodesE04B 1/3211 Structures with a vertical ...E04B 2001/3276 Panel connection detailsE04B 2001/3294 with a faceted surfaceY10S 52/10 Polyhedron
