Great snub cube

Great snub cube
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gassic
Elements
Components	3 square antiprisms
Faces	24 triangles, 6 squares
Edges	24+24
Vertices	24
Vertex figure	Isosceles 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 angles	3–3: $\arccos\left(\frac{1-2\sqrt2}{3}\right) \approx 127.55160^\circ$
	4–3: $\arccos\left(\frac{\sqrt3-\sqrt6}{3}\right) \approx 103.83616^\circ$
Central density	3
Number of external pieces	168
Level of complexity	54
Related polytopes
Army	Non-uniform Snic
Regiment	Gassic
Dual	Compound of three square antitegums
Conjugate	Great snub cube
Abstract & topological properties
Flag count	192
Orientable	Yes
Properties
Symmetry	B3+, order 24
Convex	No
Nature	Tame

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

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:

• $\left(\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{2-\sqrt2}{8}},\,\frac{\sqrt[4]{8}}{4}\right).$

Related polyhedra

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

External links

• Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#46).

• Klitzing, Richard. "gassic".

• Wikipedia Contributors. "Compound of three square antiprisms".