Great truncated cuboctahedron
{{Short description|Polyhedron with 26 faces}}
{{Uniform polyhedra db|Uniform polyhedron stat table|gtCO}}
File:Great truncated cuboctahedron.stl
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.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/20.html|title=20: great truncated cuboctahedron|last=Maeder|first=Roman|date=|website=MathConsult|url-status=dead|archive-url=https://web.archive.org/web/20200217103711/http://www.mathconsult.ch/static/unipoly/20.html|archive-date=2020-02-17|access-date=}} It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin diagram {{CDD|node_1|4|rat|d3|node_1|3|node_1}}. It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, {{CDD|node_1|4|node_1|3|node_1}}, except that the octagonal faces are replaced by {8/3} 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.
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Orthographic projections
Cartesian coordinates
Cartesian coordinates for the vertices of a great truncated cuboctahedron with side length 2 centered at the origin are all permutations of
See also
References
{{Reflist}}
External links
- {{mathworld | urlname = GreatTruncatedCuboctahedron| title = Great truncated cuboctahedron}}
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