CONVEX EQUILATERAL POLYHEDRA WITH POLYHEDRAL SYMMETRY
A new class of polyhedron is constructed by decorating each of the triangular facets of an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." A unique set of internal angles in each planar face of each new polyhedron is then obtained, for example by solving a sy...
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| creator | GAYED JAMES MAURICE SCHEIN STANLEY JAY |
| description | A new class of polyhedron is constructed by decorating each of the triangular facets of an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." A unique set of internal angles in each planar face of each new polyhedron is then obtained, for example by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, where the independent variables are a subset of the internal angles in 6 gons. Alternatively, an iterative method that solves for angles within each hexagonal ring may be solved for that nulls dihedral angle discrepancy throughout the polyhedron. The 6 gon faces in the resulting "Goldberg polyhedra" are equilateral and planar, but not equiangular, and nearly spherical. |
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A unique set of internal angles in each planar face of each new polyhedron is then obtained, for example by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, where the independent variables are a subset of the internal angles in 6 gons. Alternatively, an iterative method that solves for angles within each hexagonal ring may be solved for that nulls dihedral angle discrepancy throughout the polyhedron. The 6 gon faces in the resulting "Goldberg polyhedra" are equilateral and planar, but not equiangular, and nearly spherical.</abstract><oa>free_for_read</oa></addata></record> |
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| subjects | ADVERTISING APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND,DEAF OR MUTE BUILDING CALCULATING CEILINGS COMPUTING COUNTING CRYPTOGRAPHY DIAGRAMS DISPLAY EDUCATION EDUCATIONAL OR DEMONSTRATION APPLIANCES ELECTRIC DIGITAL DATA PROCESSING FIXED CONSTRUCTIONS FLOORS GENERAL BUILDING CONSTRUCTIONS GLOBES INSULATION OR OTHER PROTECTION OF BUILDINGS PHYSICS PLANETARIA ROOFS SEALS WALLS, e.g. PARTITIONS |
| title | CONVEX EQUILATERAL POLYHEDRA WITH POLYHEDRAL SYMMETRY |
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