Global InformationCrossed pentagrammic cupola information
| 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 | - |
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (June 2021) |
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.
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.