Triangular hebesphenorotunda
| Triangular hebesphenorotunda | |
|---|---|
 |
|
| Type |
Johnson J91 - J92 - J1 |
| Faces | 13 triangles 3 squares 3 pentagons 1 hexagon |
| Edges | 36 |
| Vertices | 18 |
| Vertex configuration | 3(33.5) 6(3.4.3.5) 3(3.5.3.5) 2.3(32.4.6) |
| Symmetry group | C3v |
| Dual polyhedron | - |
| Properties | convex |
| Net | |
 |
|
In geometry, the triangular hebesphenorotunda is one of the Johnson solids (J92).
A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.
It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. However, it does have a strong relationship to the icosidodecahedron, an Archimedean solid. Most evident is the cluster of three pentagons and four triangles on one side of the solid. If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron.
The triangular hebesphenorotunda is the only Johnson solid with faces of 3, 4, 5 and 6 sides.
The coordinates of the triangular hebesphenorotunda are:
where is the Golden Ratio.
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Wikipedia