# Great snub cube

Great snub cube Rank3
TypeUniform
SpaceSpherical
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$\sqrt{\frac{4+\sqrt2}{8}} \approx 0.82267$ Volume$\sqrt{4+3\sqrt2} \approx 2.87100$ Dihedral angles3–3: $\arccos\left(\frac{1-2\sqrt2}{3}\right) \approx 127.55160^\circ$ 4–3: $\arccos\left(\frac{\sqrt3-\sqrt6}{3}\right) \approx 103.83616^\circ$ Central density3
Number of external pieces168
Level of complexity54
Related polytopes
ArmyNon-uniform Snic
RegimentGassic
DualCompound of three square antitegums
ConjugateGreat snub cube
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.

## Vertex coordinates

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:

• $\left(\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}},\,\frac{\sqrt{8}}{4}\right).$ ## Related polyhedra

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