Great truncated cuboctahedron explained

In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U₂₀. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices.^[1] It is represented by the Schläfli symbol tr, and Coxeter-Dynkin diagram . It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron,, except that the octagonal faces are replaced by octagrams.

Convex hull

Its convex hull is a nonuniform truncated cuboctahedron. The truncated cuboctahedron and the great truncated cuboctahedron form isomorphic graphs despite their different geometric structure.

Cartesian coordinates

Cartesian coordinates for the vertices of a great truncated cuboctahedron centered at the origin are all permutations of$$\backslash Bigl(\backslash pm\; 1,\; \backslash \; \backslash pm\backslash left[1-\backslash sqrt\; 2\; \backslash right],\; \backslash \; \backslash pm\backslash left[1-2\backslash sqrt\; 2\backslash right]\backslash Bigr).$$

See also

• List of uniform polyhedra

Notes and References

1. Web site: 20: great truncated cuboctahedron. Maeder. Roman. MathConsult. dead. https://web.archive.org/web/20200217103711/http://www.mathconsult.ch/static/unipoly/20.html. 2020-02-17.