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Concept
Hemi-dodecahedron
Summary
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 is
K6 (the complete graph with 6 vertices) --- see hemi-icosahedron.
Official source
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