Crossed pentagrammic cupola
Polyhedron with 12 faces / From Wikipedia, the free encyclopedia
In geometry, the crossed pentagrammic cupola is one of the nonconvex Johnson solid isomorphs, being topologically identical to the convex pentagonal cupola. It can be obtained as a slice of the great rhombicosidodecahedron or quasirhombicosidodecahedron. As in all cupolae, the base polygon has twice as many edges and vertices as the top; in this case the base polygon is a decagram.
Quick Facts Type, Faces ...
Crossed pentagrammic cupola | |
---|---|
Type | Johnson isomorph Cupola |
Faces | 5 triangles 5 squares 1 pentagram 1 decagram |
Edges | 25 |
Vertices | 15 |
Vertex configuration | 5+5(3.4.10/3) 5(3.4.5/3.4) |
Schläfli symbol | {5/3} || t{5/3} |
Symmetry group | C5v, [5], (*55) |
Rotation group | C5, [5]+, (55) |
Dual polyhedron | - |
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It may be seen as a cupola with a retrograde pentagrammic base, so that the squares and triangles connect across the bases in the opposite way to the pentagrammic cuploid, hence intersecting each other more deeply.