| Type: | abstract regular polyhedron globally projective polyhedron |
| Schläfli: | or |
| Faces: | 4 triangles |
| Edges: | 6 |
| Vertices: | 3 |
| Symmetry: | , order 24 |
| Dual: | hemicube |
| Properties: | non-orientable |
In geometry, a hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron.
It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the hemicube.
It can be realized as a projective polyhedron (a tessellation of the real projective plane by 4 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 four equal parts. It can be seen as a square pyramid without its base.
It can be represented symmetrically as a hexagonal or square Schlegel diagram:
It has an unexpected property that there are two distinct edges between every pair of vertices – any two vertices define a digon.