Compound of three square antiprisms

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Compound of three square antiprisms
Rank3
TypeUniform
Notation
Bowers style acronymGassic
Elements
Components3 square antiprisms
Faces24 triangles, 6 squares
Edges24+24
Vertices24
Vertex figureIsosceles trapezoid, edge length 1, 1, 1, 2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–3:
 4–3:
Central density3
Number of external pieces168
Level of complexity54
Related polytopes
ArmyNon-uniform Snic, edge lengths (squares), (equilateral triangles), (between scalene triangles)
RegimentGassic
DualCompound of three square antitegums
ConjugateCompound of three square antiprisms
Abstract & topological properties
Flag count192
OrientableYes
Properties
SymmetryB3+, order 24
ConvexNo
NatureTame

The great snub cube, gassic, or compound of three square antiprisms is a uniform polyhedron compound. It consists of 24 triangles and 6 squares, with one square and three triangles joining at a vertex.

Its quotient prismatic equivalents are the small square gyroprismatic triothowedge, medial square gyroprismatic triorthowedge, great square gyroprismatic triorthowedge, small transitional square gyroprismatic triorthowedge, and great transitional square gyroprismatic triorthowedge, which are five-dimensional.

Vertex coordinates[edit | edit source]

The vertices of a great snub cube of edge length 1 are given by all even sign changes and even permutations, plus all odd sign changes and odd permutations, of:

  • .

Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the great disnub cube.

External links[edit | edit source]