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The truncated cuboctahedron is the convex hull of a rhombicuboctahedron with cubes above its 12 squares on 2-fold symmetry axes. The rest of its space can be dissected into 6 square cupolas below the octagons, and 8 triangular cupolas below the hexagons.
In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U 20. It has 26 faces (12 squares , 8 hexagons and 6 octagrams ), 72 edges, and 48 vertices. [ 1 ]
They are the cuboctahedron, truncated octahedron, truncated cube, rhombicuboctahedron, icosidodecahedron, truncated cuboctahedron, truncated icosahedron, truncated dodecahedron, and the truncated tetrahedron. [10] The dual polyhedron of an Archimedean solid is a Catalan solid. [1]
Truncated cuboctahedron (Great rhombicuboctahedron) disdyakis dodecahedron: 2 3 4| 4.6.8 O h: U11 K16 48 72 26 12{4} + 8{6} + 6{8} 16 Truncated icosidodecahedron
The truncated cuboctahedron is similar, with all regular faces, and 4.6.8 vertex figure. The triangle and squares of the rhombicuboctahedron can be independently rectified or truncated, creating four permutations of polyhedra. The partially truncated forms can be seen as edge contractions of the truncated form.
They are obtained by snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular polyhedra. The only snub polyhedron with the chiral octahedral group of symmetries is the snub cube. Only the icosahedron and the great icosahedron are also regular polyhedra.
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.
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular ), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1 , where δ S is the silver ratio, √ 2 +1.