Hemi-dodecahedron

Hemi-dodecahedron

Infobox Polyhedron



Polyhedron_Type=abstract regular polyhedron
Face_List=6 pentagons
Edge_Count=15
Vertex_Count=10
Symmetry_Group=A5
Vertex_List=5.5.5
Dual=hemi-icosahedron
Property_List= non-orientable

A hemi-dodecahedron is an abstract regular polyhedron, containing half the faces of a regular dodecahedron. It exists on a hemisphere as a projective plane where opposite points along the boundary are connected.

It has 6 pentagonal faces, 15 edges, and 10 vertices.

Petersen graph

From the point of view of graph theory this is an embedding of Petersen graph on a projective plane.With this embedding, the dual graph is K_6 (the complete graph with 6 vertices) --- see hemi-icosahedron.

See also

*57-cell - an abstract regular polychoron constructed from 57 hemi-dodecahedra.
*hemi-icosahedron


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