Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is a polyhedron with eight triangular, six square, and twelve rectangular faces. There are 24 identical vertices, with one triangle, one square, and two rectangles meeting at each one. If all the rectangles are themselves square (equivalently, all the edges are the same length, ensuring the triangles are equilateral), it is an Archimedean solid. The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids.

Rhombicuboctahedron
(Click here for rotating model)
Type	Archimedean solid Uniform polyhedron
Elements	F = 26, E = 48, V = 24 (χ = 2)
Faces by sides	8{3}+(6+12){4}
Conway notation	eC or aaC aaaT
Schläfli symbols	rr{4,3} or ${\displaystyle r{\begin{Bmatrix}4\\3\end{Bmatrix}}}$
	t0,2{4,3}
Wythoff symbol	3 4 | 2
Coxeter diagram
Symmetry group	Oh, B3, [4,3], (*432), order 48
Rotation group	O, [4,3]+, (432), order 24
Dihedral angle	3-4: 144°44′08″ (144.74°) 4-4: 135°
References	U10, C22, W13
Properties	Semiregular convex
Colored faces	3.4.4.4 (Vertex figure)
Deltoidal icositetrahedron (dual polyhedron)	Net