Hemi-dodecahedron | |
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decagonal schlegel diagram
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Type |
abstract regular polyhedron globally projective polyhedron |
Faces | 6 pentagons |
Edges | 15 |
Vertices | 10 |
Vertex configuration | 5.5.5 |
Schläfli symbol | {5,3}/2 or {5,3}5 |
Symmetry group | A5, order 60 |
Dual polyhedron | hemi-icosahedron |
Properties |
non-orientable 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 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 Petersen graph on a real projective plane. With this embedding, the dual graph is K6 (the complete graph with 6 vertices) --- see hemi-icosahedron.