# Compound of three square antiprisms

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
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${\displaystyle {\sqrt {\frac {4+{\sqrt {2}}}{8}}}\approx 0.82267}$
Volume${\displaystyle {\sqrt {4+3{\sqrt {2}}}}\approx 2.87100}$
Dihedral angles3–3: ${\displaystyle \arccos \left({\frac {1-2{\sqrt {2}}}{3}}\right)\approx 127.55160^{\circ }}$
4–3: ${\displaystyle \arccos \left({\frac {{\sqrt {3}}-{\sqrt {6}}}{3}}\right)\approx 103.83616^{\circ }}$
Central density3
Number of external pieces168
Level of complexity54
Related polytopes
ArmyNon-uniform Snic, edge lengths ${\displaystyle {\frac {\sqrt {2}}{2}}}$ (squares), ${\displaystyle {\sqrt {\frac {2-{\sqrt {1+{\sqrt {2}}}}}{2}}}}$ (equilateral triangles), ${\displaystyle {\sqrt {\frac {3-{\sqrt {2+2{\sqrt {2}}}}}{2}}}}$ (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.

## 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:

• ${\displaystyle \left({\sqrt {\frac {2+{\sqrt {2}}}{8}}},\,{\sqrt {\frac {2-{\sqrt {2}}}{8}}},\,{\frac {\sqrt[{4}]{8}}{4}}\right)}$.

## Related polyhedra

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