Hemi-octahedron

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Hemi-octahedron
Hemioctahedron.png
Type abstract regular polyhedron
globally projective polyhedron
Faces 4 triangles
Edges 6
Vertices 3
Vertex configuration 3.3.3.3
Symmetry group S4, order 24
Dual polyhedron hemicube
Properties non-orientable
Euler characteristic 1

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 seen as an square pyramid without its base. 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 has an unexpected property that there are two distinct edges between every pair of vertices – any two vertices define a digon.

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