Hemi-cuboctahedron

A hemi-cuboctahedron is an abstract polyhedron, containing half the faces of a semiregular cuboctahedron.

Hemi-cuboctahedron
Hemi-cuboctahedron.png
Typeabstract polyhedron
globally projective polyhedron
Faces7:
4 triangles
3 squares
Edges12
Vertices6
Vertex configuration3.4.3.4
Schläfli symbolr{3,4}/2 or r{3,4}3
Symmetry groupS4, order 24
Propertiesnon-orientable
Euler characteristic 1

It has 4 triangular faces and 3 square faces, 12 edges, and 6 vertices. It can be seen as a rectified hemi-octahedron or rectified hemi-cube.

It can be realized as a projective polyhedron (a tessellation of the real projective plane by 4 triangles and 3 square), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected.

DualEdit

Its dual polyhedron is a rhombic hemi-dodecahedron which has 7 vertices (1-7), 12 edges (a-l), and 6 rhombic faces (A-F).

 

Related polyhedraEdit

It has a real presentation as a uniform star polyhedron, the tetrahemihexahedron.

 

See alsoEdit

ReferencesEdit

  • McMullen, Peter; Schulte, Egon (December 2002), "6C. Projective Regular Polytopes", Abstract Regular Polytopes (1st ed.), Cambridge University Press, pp. 162–165, ISBN 0-521-81496-0

External linksEdit