Vertices 6 Schläfli symbol {3,5}/2 or {3,5}5 | Edges 15 Vertex configuration 3.3.3.3.3 | |
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Type abstract regular polyhedronglobally projective polyhedron | ||
A hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regular icosahedron. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 10 triangles), 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.
Contents
Geometry
It has 10 triangular faces, 15 edges, and 6 vertices.
It is also related to the nonconvex uniform polyhedron, the tetrahemihexahedron, which could be topologically identical to the hemi-icosahedron if each of the 3 square faces were divided into two triangles.
Graphs
It can be represented symmetrically on faces, and vertices as schlegel diagrams:
The complete graph K6
It has the same vertices and edges as the 5-dimensional 5-simplex which has a complete graph of edges, but only contains half of the (20) faces.
From the point of view of graph theory this is an embedding of