Hemi-icosahedron
Infobox Polyhedron
Polyhedron_Type=abstract regular polyhedron
Face_List=10triangle s
Edge_Count=15
Vertex_Count=6
Symmetry_Group=A5
Vertex_List=3.3.3.3.3
Dual=hemi-dodecahedron
Property_List= non-orientableA hemi-icosahedron is an abstract regular polyhedron, containing half the faces of a regularicosahedron . It exists on a hemisphere as aprojective plane where opposite points along the boundary are connected.It has 10 triangular faces, 15 edges, and 6 vertices. It has the same vertices and edges as the 5-dimensional polytope, the
5-simplex , but only contains half of the (20) faces.It is also related to the nonconvex
uniform polyhedron , thetetrahemihexahedron , which could be topologically identical to the hemi-icosahedron if each of the 3 square faces were divided into two triangles.The complete graph K6
From the point of view of
graph theory this is an embedding of (thecomplete graph with 6 vertices) on aprojective plane . With thisembedding, thedual graph is thePetersen graph --- seehemi-dodecahedron .See also
*
11-cell - an abstract regularpolychoron constructed from 11 hemi-icosahedra.
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