Hemioctahedron

Hemioctahedron
Rank	3
Type	Regular
Notation
Bowers style acronym	Elloct
Schläfli symbol	$\{3,4\}_3$
Elements
Faces	4 triangles
Edges	6
Vertices	3
Vertex figure	Square
Petrie polygons	4 triangles
Related polytopes
Dual	Hemicube (abstract)
Petrie dual	Hemioctahedron
Skewing	Hemioctahedron
Orientation double cover	Octahedron
Abstract & topological properties
Flag count	24
Euler characteristic	1
Schläfli type	{3,4}
Surface	Real projective plane
Orientable	No
Genus	1

The hemioctahedron is a regular map and abstract polytope. It is a tiling of the projective plane. It can be seen as an octahedron with antipodal points identified.

It has the property that there are two distinct edges between every pair of vertices – any two vertices define a digon. It is also self-petrial.

External links

• Klitzing, Richard. Abstract polytopes
• Hartley, Michael. "{3,4}*24".
• Wikipedia Contributors. "Hemioctahedron".

Bibliography

• McMullen, Peter; Schulte, Egon (December 2002), Abstract Regular Polytopes (1st ed.), Cambridge University Press, ISBN 0-521-81496-0