Retrohollow stellated icositetrachoric antiprism

Retrohollow stellated icositetrachoric antiprism
File:Retrohollow stellated icositetrachoric antiprism.png (OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Rahsiap
Elements
Tera	48 pentachora, 48 faceted rectified pentachora, 48 tetrahedral prisms
Cells	48+48+192 tetrahedra, 144+192 triangular prisms
Faces	192+288 triangles, 36+288 squares
Edges	144+192
Vertices	48
Measures (edge length 1)
Circumradius	√10/4 ≈ 0.79057
Height	√2/2 ≈ 0.70711
Related polytopes
Army	Icope
Regiment	Hosiap
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	F4/2×A1, order 1152
Convex	No
Nature	Wild

Vertex figure of rahsiap.

The retrohollow stellated icositetrachoric antiprism or rahsiap is a prismatic uniform polyteron consisting of 48 pentachora, 48 faceted rectified pentachora, and 48 central tetrahedral prisms; 5 pentachora, 10 faceted rectified pentachora, and 8 tetrahedral prisms meet at each vertex.

Vertex coordinates

The vertices of a retrohollow stellated icositetrachoric antiprism of edge length 1 are given by all permutations of the first four coordinates of:

• ${\biggl (}\pm {\frac {1}{2}},\pm {\frac {1}{2}},0,0,\pm {\frac {\sqrt {2}}{4}}{\biggr )}$

External links

• Bowers, Jonathan. "Miscellaneous"
• Klitzing, Richard. "Hosiap"