| Type: | Abstract regular polyhedron Globally projective polyhedron |
| Schläfli: | or |
| Faces: | 6 pentagons |
| Edges: | 15 |
| Vertices: | 10 |
| Symmetry: | , order 60 |
| Dual: | hemi-icosahedron |
| Properties: | Non-orientable |
In geometry, 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.
It can be projected symmetrically inside of a 10-sided or 12-sided perimeter:
From the point of view of graph theory this is an embedding of the Petersen graph on a real projective plane.With this embedding, the dual graph isK6 (the complete graph with 6 vertices) --- see hemi-icosahedron.