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Abstract regular polyhedron with 6 pentagonal faces From Wikipedia, the free encyclopedia
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.
Hemi-dodecahedron | |
---|---|
Type | Abstract regular polyhedron Globally projective polyhedron |
Faces | 6 pentagons |
Edges | 15 |
Vertices | 10 |
Euler char. | χ = 1 |
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 |
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 is K6 (the complete graph with 6 vertices) --- see hemi-icosahedron.
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