|Space||5-dimensional Euclidean space|
|Bowers style acronym||Ellike|
|Vertex figure||Pentagonal-pentagrammic coil|
|Petrie polygons||6 pentagonal-pentagrammic coils|
|Petrie dual||Petrial hemiicosahedron|
|Orientation double cover||Icosahedron|
|Abstract & topological properties|
|Surface||Real projective plane|
The hemiicosahedron is a regular abstract polytope and regular skew polyhedron in 5-dimensional Euclidean space. As an abstract polytope, it is a tiling of the projective plane and can be seen as an icosahedron with antipodal faces identified. It has a single faithful realization in 5-dimensional Euclidean space.
Vertex coordinates[edit | edit source]
The vertex coordinates of the hemiicosahedron in 5-dimensional Euclidean space are the same as the those of the hexateron.
Related polytopes[edit | edit source]
The hemiicosahedron can be made by subdividing the square faces of the hemicuboctahedron into triangles in a particular fashion. And likewise the hemicuboctahedron can be made by combining certain triangular faces of the hemiicosahedron into squares. This yields a embedding of the hemiicosahedron in 3-dimensional Euclidean space as a subdivision of the tetrahemihexahedron. The resulting concrete polytope is isogonal but not regular under isometry.
The skeleton of the hemiicosahedron is the complete graph , the same skeleton as the 5-simplex. This leads to a skew embedding of the hemiicosahedron in 5-dimensional Euclidean space with the same vertices and edges as the 5-simplex. This embedding is regular under isometry.
[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
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