Hemi-icosahedron
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| Hemi-icosahedron | |
|---|---|
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| Type | abstract regular polyhedron |
| Faces | 10 triangles |
| Edges | 15 |
| Vertices | 6 |
| Vertex configuration | 3.3.3.3.3 |
| Symmetry group | A5 |
| Dual | hemi-dodecahedron |
| Properties | non-orientable |
A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It exists on a hemisphere as a projective plane where opposite points along the boundary are connected.
It has 10 triangular faces, 15 edges, and 6 vertices. It has the same vertices and edges as the 5-dimensional polytope, the 5-simplex, but only contains half of the (20) faces.
It is also related to the nonconvex uniform polyhedron, the tetrahemihexahedron, which could be topologically identical to the hemi-icosahedron if each of the 3 square faces were divided into two triangles.
From the point of view of graph theory this is an embedding of K6 (the complete graph with 6 vertices) on a projective plane. With this embedding, the dual graph is the Petersen graph --- see hemi-dodecahedron.
[edit] See also
- 11-cell - an abstract regular polychoron constructed from 11 hemi-icosahedra.
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