A cat toy in the shape of a tetrakis cuboctahedron projected onto a sphereTetrakis cuboctahedrons usefully represent carbon atoms in a 3D ball-and-stick model of a diamond lattice as the normals to alternate yellow-shaded faces in the top image correspond exactly to the tetrahedral bond angles3D model of a tetrakis cuboctahedron
Its name comes from a topological construction from the cuboctahedron with the kis operator applied to the square faces. In this construction, all the vertices are assumed to be the same distance from the center, while in general octahedral symmetry can be maintain even with the 6 order-4 vertices at a different distance from the center as the other 12.
It can also be topologically constructed from the octahedron, dividing each triangular face into 4 triangles by adding mid-edge vertices (an ortho operation). From this construction, all 32 triangles will be equilateral.
This polyhedron can be confused with a slightly smaller Catalan solid, the tetrakis hexahedron, which has only 24 triangles, 32 edges, and 14 vertices.
Octahedron with edges bisected and faces divided into subtriangles of the tetrakis cuboctahedron
tetrakis, cuboctahedron, geometry, tetrakis, cuboctahedron, convex, polyhedron, with, triangular, faces, edges, vertices, dual, truncated, rhombic, dodecahedron, typegeodesic, polyhedron, faces32, triangles, types, edges48, types, vertices18, types, vertex, co. In geometry the tetrakis cuboctahedron is a convex polyhedron with 32 triangular faces 48 edges and 18 vertices It is a dual of the truncated rhombic dodecahedron Tetrakis cuboctahedronTypeGeodesic polyhedron 2 0 Faces32 triangles 2 types Edges48 2 types Vertices18 2 types Vertex configuration 6 35 12 36Conway notationk4aCSymmetry groupOctahedral Oh Dual polyhedronchamfered cubePropertiesconvexNet A cat toy in the shape of a tetrakis cuboctahedron projected onto a sphere Tetrakis cuboctahedrons usefully represent carbon atoms in a 3D ball and stick model of a diamond lattice as the normals to alternate yellow shaded faces in the top image correspond exactly to the tetrahedral bond angles 3D model of a tetrakis cuboctahedron Its name comes from a topological construction from the cuboctahedron with the kis operator applied to the square faces In this construction all the vertices are assumed to be the same distance from the center while in general octahedral symmetry can be maintain even with the 6 order 4 vertices at a different distance from the center as the other 12 Contents 1 Related polyhedra 2 See also 3 References 4 External linksRelated polyhedra editIt can also be topologically constructed from the octahedron dividing each triangular face into 4 triangles by adding mid edge vertices an ortho operation From this construction all 32 triangles will be equilateral This polyhedron can be confused with a slightly smaller Catalan solid the tetrakis hexahedron which has only 24 triangles 32 edges and 14 vertices nbsp Octahedron with edges bisected and faces divided into subtriangles of the tetrakis cuboctahedron nbsp Cuboctahedron nbsp Tetrakis hexahedron nbsp The nonconvex octahemioctahedron looks like a concave tetrakis cuboctahedron with inverted square pyramids meeting at the polyhedron center See also editPentakis icosidodecahedronReferences editJohn H Conway Heidi Burgiel Chaim Goodman Strauss The Symmetries of Things 2008 ISBN 978 1 56881 220 5 Chapter 21 Naming the Archimedean and Catalan polyhedra and Tilings p284 External links editVTML polyhedral generator Try k4aC Conway polyhedron notation Retrieved from https en wikipedia org w index php title Tetrakis cuboctahedron amp oldid 1197351913, wikipedia, wiki, book, books, library,
