Snub cube

Snub cube
Snub cube, left-chiral and right-chiral
Type	Archimedean solid
Faces	38
Edges	60
Vertices	24
Symmetry group	Rotational octahedral symmetry ${\displaystyle \mathrm {O} }$
Dihedral angle (degrees)	triangle-to-triangle: 153.23° triangle-to-square: 142.98°
Dual polyhedron	Pentagonal icositetrahedron
Properties	convex, chiral
Vertex figure
Net

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. 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 ${\displaystyle t\scriptstyle {\begin{Bmatrix}4\\3\end{Bmatrix}}}$.

The snub cube, like the snub dodecahedron, is chiral, which means it does not equal its mirror image; it has two equally valid forms.