|Type||abstract regular polyhedron
globally projective polyhedron
|Symmetry group||A5, order 60|
Euler characteristic 1
A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 10 triangles), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into three equal parts.
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.
The complete graph K6
From the point of view of graph theory this is an embedding of (the complete graph with 6 vertices) on a real projective plane. With this embedding, the dual graph is the Petersen graph --- see hemi-dodecahedron.
- 11-cell - an abstract regular polychoron constructed from 11 hemi-icosahedra.
- McMullen, Peter; Schulte, Egon (December 2002), "6C. Projective Regular Polytopes", Abstract Regular Polytopes (1st ed.), Cambridge University Press, pp. 162–165, ISBN 0-521-81496-0
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