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In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It is represented by Schläfli symbol tr{4/3,3}, 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 {8/3} octagrams.
Contents
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
(±1, ±(1−√2), ±(1−2√2)).References
Great truncated cuboctahedron Wikipedia(Text) CC BY-SA