Cuboctahedron

The cuboctahedron is a quasiregular polyhedron and one of the 13 Archimedean solids. It consists of 8 equilateral triangles and 6 squares, with two of each joining at a vertex. It can be derived as a rectified cube or octahedron.

The cuboctahedron has the rare property that its circumradius equals its edge length. Other notable polytopes that satisfy this property are the hexagon, the tesseract, and the icositetrachoron.

Vertex coordinates
A cuboctahedron of side length 1 has vertex coordinates given by all permutations of
 * (±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0).

Rhombitetratetrahedron
A cuboctahedron can also be constructed in A3 symmetry, as the cantellated tetrahedron. In this form, the 8 triangles split into 2 sets of 4, and the squares alternately join to the two kinds of triangles. It can be represented as o3x3o.