Patent US3646718A successfully refreshed from Google Patents.
US3646718A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Polyhedral structural system and spatial enclosure
Assignee: Individual
•
Filing: 1969-07-03
•
Granted: 1972-03-07
•
Expires: 1989-07-03
Abstract
Abstract A structural system and spatial enclosure defined by a new polyhedron, the isoicosahedron, having 20 faces consisting of eight hexagons and 12 pentagons, 54 straight line elements, and 36 vertices, which, in a preferred form, lie on the surface of an imaginary sphere circumscribing the polyhedron. In the preferred form, the hexagons are regular and congruent while the pentagons though congruent are irregular having three sides equal in length to the side length of the hexagons and two sides equal to said length divided by the square root 2. In other forms, the 36 vertices of the polyhedron lie on the surface of an imaginary enclosing spheroid, oblate, elongate, or irregular. The isoicosahedra form modular units which can be reiterated in a building structure. The packed modular polyhedra define unique polyhedral spaces each having nine faces consisting of six pentagons and three squares, the endoenneahedron.
Inventors
- 👤 John E Mckenna
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 04:38
CPC Classifications
E; E04; E04B; E04B1/00; E04B1/348; E04B1/34815; E04B2001/0053; Y; Y10; Y10S; Y10S52/00; Y10S52/10
Claims Analysis
Total Claims: 4
Claim 1
Independent Claim
328 words
A building structure formed of a plurality of modular elements comprising: a plurality of first polyhedral elements, each having 20 faces comprising eight hexagons and 12 pentagons, 54 straight-line edge elements defining the faces, and 36 vertices, said faces arranged in a first ring of six side-by-side hexagons, second and third rings of six side-by-side pentagons adjacent either side of the first ring, said second and third rings each surrounding a hexagon on the side away from the first ring, said eight hexagons bring regular and congruent and said 12 pentagons being irregular and congruent, each said pentagon formed with three edges of a first length equal to an edge length of said hexagons and wherein the other two edges are formed with a second length equal to said first length divided by square root 2, said two edges of the second length separated by edges of the first length, and wherein the 36 vertices lie on the surface of an imaginary sphere circumscribing the polyhedral element, the ratio of the radius of said sphere to one-half the edge length of said hexagon being substantially equal to square root 13; said plurality of first polyhedral elements arranged side by side in a three-dimensional array with hexagonal faces in adjacent relationship; and a plurality of second polyhedral elements defined by the interspaces between said plurality of first polyhedral elements, each said second polyhedral element having nine faces comprising six pentagons and three squares, said faces arranged so that each square is surrounded by four pentagons, said six pentagons being irregular and congruent, each said pentagon also being congruent with the pentagons comprising said first polyhedral elements and wherein the vertices of each second polyhedral element lie in the surface of an imaginery sphere circumscribing the second polyhedral element, the ratio of the radius of the sphere circumscribing the first polyhedral element to the radius of the sphere circumscribing the second polyhedral element being substantially equal to square root 13/2.
Claim 2
Dependent Claim
328 words
A building structure formed of a plurality of modular elements comprising: a plurality of first polyhedral elements, each having 20 faces comprising eight hexagons and 12 pentagons, 54 straight-line edge elements defining the faces, and 36 vertices, said faces arranged in a first ring of six side-by-side hexagons, second and third rings of six side-by-side pentagons adjacent either side of the first ring, said second and third rings each surrounding a hexagon on the side away from the first ring, said eight hexagons bring regular and congruent and said 12 pentagons being irregular and congruent, each said pentagon formed with three edges of a first length equal to an edge length of said hexagons and wherein the other two edges are formed with a second length equal to said first length divided by square root 2, said two edges of the second length separated by edges of the first length, and wherein the 36 vertices lie on the surface of an imaginary sphere circumscribing the polyhedral element, the ratio of the radius of said sphere to one-half the edge length of said hexagon being substantially equal to square root 13; said plurality of first polyhedral elements arranged side by side in a three-dimensional array with hexagonal faces in adjacent relationship; and a plurality of second polyhedral elements defined by the interspaces between said plurality of first polyhedral elements, each said second polyhedral element having nine faces comprising six pentagons and three squares, said faces arranged so that each square is surrounded by four pentagons, said six pentagons being irregular and congruent, each said pentagon also being congruent with the pentagons comprising said first polyhedral elements and wherein the vertices of each second polyhedral element lie in the surface of an imaginery sphere circumscribing the second polyhedral element, the ratio of the radius of the sphere circumscribing the first polyhedral element to the radius of the sphere circumscribing the second polyhedral element being substantially equal to square root 13/2.
Claim 3
Dependent Claim
267 words
A building structure formed of a plurality of modular elements comprising: a plurality of first polyhedral elements, each having 20 faces comprising 8 hexagons and 12 pentagons, 54 straight-line edge elements defining the faces, and 36 vertices, said faces arranged in a first ring of six side-by-side hexagons, second and third rings of six side-by-side pentagons adjacent either side of the ring, said second and third rings each surrounding a hexagon on the side away from the first ring, said eight hexagons being regular and congruent and said 12 pentagons being irregular and congruent, each said pentagon formed with three edges of a first length equal to an edge length of said hexagons and wherein the other two edges are formed with a second length equal to said first length divided by Square Root 2, said two edges of the second length separated by edges of the first length, and wherein the 36 vertices lie on the surface of an imaginary sphere circumscribing the polyhedral element, the ratio of the radius of said sphere to one-half the edge length of said hexagon being substantially equal to Square Root 13; said plurality of first polyhedral elements arranged side-by-side in a three-dimensional array with hexagonal faces in adjacent relationship whereby the modular polyhedral elements define interspaces substantially enclosed by the pentagonal faces of the polyhedral elements with square holes opening between the interspaces and to the exterior of the building structure and wherein the building structure also includes flat, rectangular faces closing the square holes between the interspaces and between the interspaces and the exterior of the building structure.
Claim 4
Dependent Claim
267 words
A building structure formed of a plurality of modular elements comprising: a plurality of first polyhedral elements, each having 20 faces comprising 8 hexagons and 12 pentagons, 54 straight-line edge elements defining the faces, and 36 vertices, said faces arranged in a first ring of six side-by-side hexagons, second and third rings of six side-by-side pentagons adjacent either side of the ring, said second and third rings each surrounding a hexagon on the side away from the first ring, said eight hexagons being regular and congruent and said 12 pentagons being irregular and congruent, each said pentagon formed with three edges of a first length equal to an edge length of said hexagons and wherein the other two edges are formed with a second length equal to said first length divided by Square Root 2, said two edges of the second length separated by edges of the first length, and wherein the 36 vertices lie on the surface of an imaginary sphere circumscribing the polyhedral element, the ratio of the radius of said sphere to one-half the edge length of said hexagon being substantially equal to Square Root 13; said plurality of first polyhedral elements arranged side-by-side in a three-dimensional array with hexagonal faces in adjacent relationship whereby the modular polyhedral elements define interspaces substantially enclosed by the pentagonal faces of the polyhedral elements with square holes opening between the interspaces and to the exterior of the building structure and wherein the building structure also includes flat, rectangular faces closing the square holes between the interspaces and between the interspaces and the exterior of the building structure.
References Cited (Backward Citations)
US1425114A
Cited
FR900229A
Cited
US2922299A
Cited
US2795893A
Cited
GB1043396A
Cited
US3230673A
Cited
FR1443198A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-03-07 | 1975-09-06 | 1976-03-07 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-03-07 | 1979-09-06 | 1980-03-07 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-03-07 | 1983-09-06 | 1984-03-07 | $7700.00 | Window Closed / Lapsed |