Snub cube

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices.

Snub cube
(Click here for rotating model)
Type	Archimedean solid Uniform polyhedron
Elements	F = 38, E = 60, V = 24 (χ = 2)
Faces by sides	(8+24){3}+6{4}
Conway notation	sC
Schläfli symbols	sr{4,3} or ${\displaystyle s{\begin{Bmatrix}4\\3\end{Bmatrix}}}$
	ht0,1,2{4,3}
Wythoff symbol	| 2 3 4
Coxeter diagram
Symmetry group	O, 1/2B3, [4,3]+, (432), order 24
Rotation group	O, [4,3]+, (432), order 24
Dihedral angle	3-3: 153°14′04″ (153.23°) 3-4: 142°59′00″ (142.98°)
References	U12, C24, W17
Properties	Semiregular convex chiral
Colored faces	3.3.3.3.4 (Vertex figure)
Pentagonal icositetrahedron (dual polyhedron)	Net

It is a chiral polyhedron; that is, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub cubes, and the convex hull of both sets of vertices is a truncated cuboctahedron.

Kepler first named it in Latin as cubus simus in 1619 in his Harmonices Mundi. H. S. M. Coxeter, noting it could be derived equally from the octahedron as the cube, called it snub cuboctahedron, with a vertical extended Schläfli symbol ${\displaystyle s\scriptstyle {\begin{Bmatrix}4\\3\end{Bmatrix}}}$, and representing an alternation of a truncated cuboctahedron, which has Schläfli symbol ${\displaystyle t\scriptstyle {\begin{Bmatrix}4\\3\end{Bmatrix}}}$.