Retrograde pentagrammic cupola
|Retrograde pentagrammic cupola|
|Bowers style acronym||Rastacu|
|Faces||5 triangles, 5 squares, 1 pentagram, 1 decagram|
|Vertex figures||5 crossed isosceles trapezoids, edge lengths 1, √2, (1-√5)/2, √2|
|10 scalene triangles, edge lengths 1, √2, √(5-√5)/2|
|Measures (edge length 1)|
|Dual||Semibisected pentagrammic trapezohedron|
|Convex hull||Pentagonal cupola|
|Abstract & topological properties|
|Symmetry||H2×I, order 10|
The retrograde pentagrammic cupola or rastacu, also called the crossed pentagrammic cupola or sometimes just the pentagrammic cupola, is a cupola based on the pentagram, seen as a 5/3-gon rather than 5/2. It consists of 5 triangles, 5 squares, 1 pentagram, and 1 decagram.
It can be obtained as a segment of the quasirhombicosidodecahedron, just as its conjugate, the convex pentagonal cupola, can be obtained from the small rhombicosidodecahedron.
It also appears in some scaliform polychora, namely the retroprismatorhombisnub hecatonicosachoron and retroprismatorhombiretrosnub hecatonicosachoron.
Vertex coordinates[edit | edit source]
A retrograde pentagrammic cupola of edge length 1 has vertices given by the following coordinates:
Related polyhedra[edit | edit source]
The retrograde pentagrammic cupola is the pentagram-first cap of the quasirhombicosidodecahedron.
External links[edit | edit source]
- Klitzing, Richard. "rastacu".