Great complex icosidodecahedron
{{Short description|Degenerate uniform star polyhedron}}
{{Uniform polyhedra db|Uniform polyhedron stat table|Gacid}}
In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.
It can be constructed from a number of different vertex figures.
As a compound
The great complex icosidodecahedron can be considered a compound of the small stellated dodecahedron, {5/2,5}, and great icosahedron, {3,5/2}, sharing the same vertices and edges, while the second is hidden, being completely contained inside the first.
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See also
References
- {{Citation | last1=Coxeter | first1=Harold Scott MacDonald | author1-link=Harold Scott MacDonald Coxeter | last2=Longuet-Higgins | first2=M. S. | last3=Miller | first3=J. C. P. | title=Uniform polyhedra | jstor=91532 | mr=0062446 | year=1954 | journal=Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences | issn=0080-4614 | volume=246 | issue=916 | pages=401–450 | doi=10.1098/rsta.1954.0003| bibcode=1954RSPTA.246..401C | s2cid=202575183 }} (Table 6, degenerate cases)
- {{mathworld | urlname = GreatComplexIcosidodecahedron| title = Great complex icosidodecahedron}}
- {{KlitzingPolytopes|polyhedra-neu.htm|3D uniform polyhedra|o5/3x3o5*a and o3/2x5/2o5*a - gacid}}