Hemioctahedron

From Polytope Wiki
Jump to navigation Jump to search
Hemioctahedron
Rank3
TypeRegular
Notation
Bowers style acronymElloct
Schläfli symbol[1]
Elements
Faces4 triangles
Edges6
Vertices3
Vertex figureSquare
Petrie polygons4 triangles
Related polytopes
DualHemicube (abstract)
Petrie dualHemioctahedron
SkewingHemioctahedron
Orientation double coverOctahedron
Abstract & topological properties
Flag count24
Euler characteristic1
Schläfli type{3,4}
SurfaceReal projective plane[1]
OrientableNo
Genus1

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[edit | edit source]

References[edit | edit source]

Bibliography[edit | edit source]

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