Cuboctahedron

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is radially equilateral.

Cuboctahedron
(Click here for rotating model)
Type	Archimedean solid Uniform polyhedron
Elements	F = 14, E = 24, V = 12 (χ = 2)
Faces by sides	8{3}+6{4}
Conway notation	aC aaT
Schläfli symbols	r{4,3} or ${\displaystyle {\begin{Bmatrix}4\\3\end{Bmatrix}}}$ rr{3,3} or ${\displaystyle r{\begin{Bmatrix}3\\3\end{Bmatrix}}}$
	t1{4,3} or t0,2{3,3}
Wythoff symbol	2 | 3 4 3 3 | 2
Coxeter diagram	or or
Symmetry group	Oh, B3, [4,3], (*432), order 48 Td, [3,3], (*332), order 24
Rotation group	O, [4,3]+, (432), order 24
Dihedral angle	${\displaystyle \operatorname {arcsec} \left(-{\sqrt {3}}\right)\approx 125.26^{\circ }}$
References	U07, C19, W11
Properties	Semiregular convex quasiregular
Colored faces	3.4.3.4 (Vertex figure)
Rhombic dodecahedron (dual polyhedron)	Net

Its dual polyhedron is the rhombic dodecahedron.

The cuboctahedron was probably known to Plato: Heron's Definitiones quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares.