Sphere-dome construction

Claim 2

A self-supporting sphere-approximating structure comprising, interconnected structural elements forming twelve equal regular pentagons having their centers located at the vertexes of a regular icosahedron, and, for a sphere approximation of order 1, 60 hexagons; and for a sphere approximation of order k, Nk hexagons at least some of which depart from regular hexagons to enable contiguity of adjacent ones of said structural elements, where k is an integer greater than 1, where Nk equals 3Nk 1 + 20, and where Nk 1 is the number of hexagons for a sphere approximation of order one less than k.

Claim 3

A self-supporting sphere-approximating structure, comprising interconnected structural elements forming twelve equal regular pentagons and n hexagons at least some of which hexagons are irregular to enable contiguity of adjacent modules, the centers of the pentagons defining vertexes of a regular icosahedron, where n is an integer selected from the following group: 60, 200, and 620.

Claim 4

A self-supporting sphere-approximating structure, comprising interconnected structural elements forming twelve equal regular pentagons and n hexagons at least some of which hexagons are irregular to enable contiguity of adjacent modules, the centers of the pentagons defining vertexes of a regular icosahedron, where n is an integer selected from the following group: 60, 200, and 620.

Claim 5

A structure as defined in claim 2 wherein the structural elements are planar pentagonal and hexagonal modules.

Claim 6

A structure as defined in claim 2 wherein the structural elements are ribs which lie along the edges of the hexagons and pentagons.

Claim 7

A structure as defined in claim 2, wherein n 60 and all of the hexagons are of the same size and the same shape.

Claim 8

A structure as defined in claim 2, wherein n 200 and 80 hexagons are regular and of equal size, while 60 hexagons are of a first predetermined size and shape, and 60 hexagons are of a second predetermined size and shape.

Claim 9

A structure as defined in claim 5 wherein a circle may be inscribed in each hexagon and in each pentagon, and the structural elements are aligned such that circles inscribed in the hexagons and pentagons would be tangent to a common sphere.

Claim 10

A structure as defined in claim 6 wherein the structural elements are aligned such that closed curved figures, selected from the class of figures comprising circles and approximate circles, inscribed in the hexagons and pentagons, would be approximately tangent to a common sphere.

Claim 11

A structure as defined in claim 6 wherein the arrangement of the structural elements is obtained substantially by triangulation of that structure obtained where the following conditions are satisfied: n is selected to be 60 and all of the hexagons are of the same size and same shape.

Claim 12

A structure as defined in claim 2 wherein the angle between the line joining the center of any of said pentagons to a vertex of a dodecahedron corresponding in invert relationship to said icosahedron and the line joining the center of the last mentioned pentagon to the vertex of the pentagon nearest said dodecahedron vertex is substantially 13*6''.

Claim 13

A structure as defined in claim 2, wherein n 620 and the arrangement of the structural elements is obtained by triangulation from that structure wherein n 60.

Claim 14

A structure as defined in claim 2, wherein all of the interior angles of all of the irregular hexagons lie in the range 114* to 126*.

Claim 15

A segment of a self-supporting sphere-approximating structure comprising, in its complete sphere-approximating version, interconnected structural elements forming twelve equal regular pentagons having their centers located at the vertexes of a regular icosahedron, and, for a sphere approximation of order 1, 60 hexagons; and for a sphere approximation of order k, Nk hexagons at least some of which depart from regular hexagons to enable contiguity of adjacent ones of said structural elements, where k is an integer greater than 1, where Nk equals 3Nk 1 + 20, and where Nk 1 is the number of hexagons for a sphere approximation of order one less than k.

Claim 16

A segment of a self-supporting sphere-approximating structure comprising, in its complete sphere-approximating version, interconnected structural elements forming twelve equal regular pentagons having their centers located at the vertexes of a regular icosahedron, and, for a sphere approximation of order 1, 60 hexagons; and for a sphere approximation of order k, Nk hexagons at least some of which depart from regular hexagons to enable contiguity of adjacent ones of said structural elements, where k is an integer greater than 1, where Nk equals 3Nk 1 + 20, and where Nk 1 is the number of hexagons for a sphere approximation of order one less than k.

Claim 17

The structure defined in claim 13 wherein the segment approximates a dome shape.

Claim 18

A segment of a self-supporting sphere-approximating structure comprising in its whole version, interconnected structural elements forming twelve equal regular pentagons and n hexagons at least some of which hexagons are irregular to enable contiguity of adjacent modules, the centers of the pentagons defining vertexes of a regular icosahedron, where n is an integer selected from the following group: 60, 200, and 620.

Claim 19

A segment of a self-supporting sphere-approximating structure comprising in its whole version, interconnected structural elements forming twelve equal regular pentagons and n hexagons at least some of which hexagons are irregular to enable contiguity of adjacent modules, the centers of the pentagons defining vertexes of a regular icosahedron, where n is an integer selected from the following group: 60, 200, and 620.

Claim 20

A structure as defined in claim 15, wherein n 620 and the arrangement of the structural elements is obtained by triangulation from that structure wherein n 60.

Claim 21

A structure as defined in claim 15, wherein all of the interior angles of all of the irregular hexagons lie in the range 114* to 126*.

Claim 22

The structure defined in claim 17 wherein the segment approximates a dome shape.

Claim 23

A structure as defined in claim 18 wherein the structural elements are planar pentagonal and hexagonal modules.

Claim 24

A structure as defined in claim 18, wherein the structural elements are ribs which lie along the edges of the hexagons and pentagons.

Claim 25

A structure as defined in claim 18, wherein n 60 and all of the hexagons are of the same size and the same shape.

Claim 26

A structure as defined in claim 21 wherein a circle may be inscribed in each hexagon and in each pentagon, and the structural elements are aligned such that circles inscribed in the hexagons and pentagons would be tangent to a common sphere.

Claim 27

A structure as defined in claim 18, wherein n 200 and 80 hexagons are regular and of equal size, while 60 hexagons are of a first predetermined size and shape, and 60 hexagons are of a second predetermined size and shape.

Claim 28

A structure as defined in claim 23 wherein the structural elements are aligned such that closed curved figures, selected from the class of figures comprising circles and approximate circles, inscribed in the hexagons and pentagons, would be approximately tangent to a common sphere.

Claim 29

A structure as defined in claim 23 wherein the arrangement of the structural elements is obtained substantially by triangulation of that structure obtained where the following conditions are satisfied: n is selected to be 60 and all of the hexagons are of the same size and same shape.

Claim 30

A structure as defined in claim 18 wherein the angle between the line joining the center of any of said pentagons to a vertex of the invert dodecahedron corresponding to the said icosahedron and the line joining the center of the last mentioned pentagon to the vertex of the last mentioned pentagon nearest said invert dodecahedron vertex is substantially 13*6''.