great cubicuboctahedron
{{Uniform polyhedra db|Uniform polyhedron stat table|gCCO}}
File:Great cubicuboctahedron.stl
In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices.{{Cite web|url=https://www.mathconsult.ch/static/unipoly/14.html|title=14: great cubicuboctahedron|last=Maeder|first=Roman|date=|website=MathConsult}} Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The prefix great serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.{{Cite web|url=https://www.software3d.com/GreatCubicubocta.php|title=Great Cubicuboctahedron|last=Webb|first=Robert|date=|website=Stella: Polyhedron Navigator}}
Orthographic projections
Related polyhedra
It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having the octagrammic faces in common).
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= Great hexacronic icositetrahedron=
{{Uniform polyhedra db|Uniform dual polyhedron stat table|gCCO}}
File:Great hexacronic icositetrahedron.stl
The great hexacronic icositetrahedron (or great lanceal disdodecahedron) is the dual of the great cubicuboctahedron.
See also
References
{{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 | doi=10.1017/CBO9780511569371}}
External links
- {{mathworld | urlname = GreatCubicuboctahedron| title =Great cubicuboctahedron}}
- {{mathworld|urlname= GreatHexacronicIcositetrahedron|title= Great Hexacronic Icositetrahedron}}
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