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Crossed pentagonal cuploid
Polyhedron with 11 faces / From Wikipedia, the free encyclopedia
In geometry, the crossed pentagonal cuploid or crossed pentagonal semicupola is one member of the infinite family of cuploids. It can be obtained as a slice of the great complex rhombicosidodecahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; but in this case the base polygon is a degenerate {10/4} decagram, as the top is a {5/4} pentagon. Hence, the degenerate base is withdrawn and the triangles are connected to the squares instead.
Quick Facts Faces, Edges ...
Crossed pentagonal cuploid | |
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Faces | 5 triangles 5 squares 1 pentagon |
Edges | 20 |
Vertices | 10 |
Vertex configuration | 5(5.4.3/2.4) 5(3.4.3/2.4/3) |
Symmetry group | C5v, [5], (*55) |
Rotation group | C5, [5]+, (55) |
Dual polyhedron | crossed pentagonal keratinoid |
Properties | non-orientable |
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It may be seen as a cupola with a retrograde pentagonal base, so that the squares and triangles connect across the bases in the opposite way to the pentagonal cupola, hence intersecting each other.