Pentagrammic cuploid
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Pentagrammic cuploid | |
---|---|
Rank | 3 |
Type | Segmentotope |
Notation | |
Bowers style acronym | Stiscu |
Elements | |
Faces | 5 triangles, 5 squares, 1 pentagram |
Edges | 5+5+10 |
Vertices | 5+5 |
Vertex figures | 5 isosceles trapezoids, edge lengths 1, √2, (1-√5)/2, √2 |
5 butterflies, edge lengths 1, √2, 1, √2 | |
Measures (edge length 1) | |
Circumradius | |
Dihedral angles | 5/2–4: |
3–4: | |
Height | |
Related polytopes | |
Army | Pentagonal antipodium |
Conjugate | Retrograde pentagonal cuploid |
Abstract & topological properties | |
Euler characteristic | 1 |
Orientable | No |
Genus | 1 |
Properties | |
Symmetry | H2×I, order 10 |
Convex | No |
Nature | Tame |
The pentagrammic cuploid, also called the pentagrammic semicupola or stiscu, is an orbiform polyhedron. It consists of 5 triangles, 5 squares, and 1 pentagram. It is a cuploid based on the pentagram {5/2}, with a pseudo {10/2} base (corresponding to a doubled-up pentagon which is blended out).
Vertex coordinates[edit | edit source]
A pentagrammic cuploid of edge length 1 has vertices given by the following coordinates:
Related polyhedra[edit | edit source]
The pentagrammic cuploid can be edge-inscribed into the small ditrigonary icosidodecahedron; it uses its triangles and pentagrams as well as squares of the rhombihedron, the inscribed compound of 5 cubes.
External links[edit | edit source]
- Klitzing, Richard. "stiscu".
- Wikipedia contributors. "Pentagrammic cuploid".