Truncated cuboctahedron

Truncated cuboctahedron
(Click here for rotating model)
Type	Archimedean solid Uniform polyhedron
Elements	F = 26, E = 72, V = 48 (χ = 2)
Faces by sides	12{4}+8{6}+6{8}
Conway notation	bC or taC
Schläfli symbols	tr{4,3} or ${\displaystyle t{\begin{Bmatrix}4\\3\end{Bmatrix}}}$
	t0,1,2{4,3}
Wythoff symbol	2 3 4 |
Coxeter diagram
Symmetry group	Oh, B3, [4,3], (*432), order 48
Rotation group	O, [4,3]+, (432), order 24
Dihedral angle	${\displaystyle {\begin{aligned}{\text{4-6:}}&\ \arccos {\tfrac {-{\sqrt {6}}}{3}}=144^{\circ }44'08''\\[4pt]{\text{4-8:}}&\ \arccos {\tfrac {-1}{\sqrt {2}}}=135^{\circ }\\{\text{6-8:}}&\ \arccos {\tfrac {-{\sqrt {3}}}{3}}=125^{\circ }15'51''\end{aligned}}}$
References	U11, C23, W15
Properties	Semiregular convex zonohedron
Colored faces	4.6.8 (Vertex figure)
Disdyakis dodecahedron (dual polyhedron)	Net

In geometry, the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It has 12 square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices, and 72 edges. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated cuboctahedron is a 9-zonohedron. The truncated cuboctahedron can tessellate with the octagonal prism.