| Type: | abstract regular polyhedron globally projective polyhedron |
| Schläfli: | or |
| Faces: | 10 triangles |
| Edges: | 15 |
| Vertices: | 6 |
| Symmetry: | , order 60 |
| Dual: | hemi-dodecahedron |
| Properties: | non-orientable |
In geometry, 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.
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.
It can be represented symmetrically on faces, and vertices as Schlegel diagrams:
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
K6