|Type||abstract regular polyhedron
globally projective polyhedron
|Symmetry group||A5, order 60|
Euler characteristic 1
A hemi-dodecahedron is an abstract regular polyhedron, containing half the faces of a regular dodecahedron. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 6 pentagons), 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 6 pentagonal faces, 15 edges, and 10 vertices.
From the point of view of graph theory this is an embedding of Petersen graph on a real projective plane. With this embedding, the dual graph is K6 (the complete graph with 6 vertices) --- see hemi-icosahedron.
- 57-cell – an abstract regular polychoron constructed from 57 hemi-dodecahedra.
- 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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