Tridiminished icosahedron
| Tridiminished icosahedron | |
|---|---|
 | |
| Type |
Johnson J62 - J63 - J64 |
| Faces |
2+3 triangles 3 pentagons |
| Edges | 15 |
| Vertices | 9 |
| Vertex configuration |
2x3(3.52) 3(33.5) |
| Symmetry group | C3v |
| Dual polyhedron | Dual of tridiminished icosahedron (unnamed enneahedron) |
| Properties | convex |
| Net | |
 | |
In geometry, the tridiminished icosahedron is one of the Johnson solids (J63).
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.[1]
The name refers to one way of constructing it, by removing three pentagonal pyramids from a regular icosahedron, which replaces three sets of five triangular faces from the icosahedron with three mutually adjacent pentagonal faces.
Related polytopes
The tridiminished icosahedron is the vertex figure of the snub 24-cell, a uniform 4-polytope (4-dimensional polytope).
See also
- Diminished icosahedron (J11)
- Metabidiminished icosahedron (J62)
External links
- Eric Wolfgang Weisstein, Tridiminished icosahedron (Johnson Solid) at MathWorld.
- ↑ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, MR 0185507, Zbl 0132.14603, doi:10.4153/cjm-1966-021-8.
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