Cubitruncated cuboctahedron

Its convex hull is a nonuniform truncated cuboctahedron.

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Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of

: (±({{radic|2}}−1), ±1, ±({{radic|2}}+1))

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{{Uniform polyhedra db|Uniform dual polyhedron stat table|ctCO}}

File:Tetradyakis hexahedron.stl

The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.

The triangles have one angle of $\backslash arccos(\backslash frac\{3\}\{4\})\backslash approx\; 41.409\backslash ,622\backslash ,109\backslash ,27^\{\backslash circ\}$, one of $\backslash arccos(\backslash frac\{1\}\{6\}+\backslash frac\{7\}\{12\}\backslash sqrt\{2\})\backslash approx\; 7.420\backslash ,694\backslash ,647\backslash ,42^\{\backslash circ\}$ and one of $\backslash arccos(\backslash frac\{1\}\{6\}-\backslash frac\{7\}\{12\}\backslash sqrt\{2\})\backslash approx\; 131.169\backslash ,683\backslash ,243\backslash ,31^\{\backslash circ\}$. The dihedral angle equals $\backslash arccos(-\backslash frac\{5\}\{7\})\backslash approx\; 135.584\backslash ,691\backslash ,402\backslash ,81^\{\backslash circ\}$. Part of each triangle lies within the solid, hence is invisible in solid models.

It is the dual of the uniform cubitruncated cuboctahedron.

• List of uniform polyhedra

{{Reflist}}

• {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}} p. 92

• {{mathworld | urlname = CubitruncatedCuboctahedron| title = Cubitruncated cuboctahedron}}
• {{mathworld | urlname = TetradyakisHexahedron| title =Tetradyakis hexahedron}}
• [http://gratrix.net/polyhedra/uniform/summary/ http://gratrix.net Uniform polyhedra and duals]

Category:Uniform polyhedra

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