|Bowers style acronym||Starp|
|Coxeter diagram||s2s10/3o ()|
|Faces||10 triangles, 2 pentagrams|
|Vertex figure||Crossed isosceles trapezoid, edge lengths 1, 1, 1, (√5–1)/2|
|Measures (edge length 1)|
|Number of external pieces||72|
|Level of complexity||24|
|Dual||Pentagrammic concave antitegum|
|Convex core||Pentagonal antitegum|
|Abstract & topological properties|
|Symmetry||I2(10)×A1/2, order 20|
The pentagrammic retroprism, or starp, also called the pentagrammic crossed antiprism, is a prismatic uniform polyhedron. It consists of 10 triangles and 2 pentagrams. Each vertex joins one pentagram and three triangles. As the name suggests, it is a crossed antiprism based on a pentagram, seen as a 5/3-gon rather than 5/2. This makes it the simplest uniform crossed antiprism.
Similar to how the pentagonal antiprism can be edge-inscribed into the regular icosahedron, the pentagrammic retroprism can be edge-inscribed into a great icosahedron. It can be constructed by diminishing two opposite vertices of the great icosahedron.
Vertex coordinates[edit | edit source]
A pentagrammic retroprism of edge length 1 has vertex coordinates given by:
These coordinates are obtained by removing two opposite vertices from a great icosahedron.
An alternative set of coordinates can be constructed in a similar way to other polygonal antiprisms, giving the vertices as the following points along with their central inversions:
Related polyhedra[edit | edit source]
Two non-prismatic uniform polyhedron compounds are composed of pentagrammic retroprisms:
There are also an infinite amount of prismatic uniform compounds that are the crossed antiprisms of compounds of pentagrams.
External links[edit | edit source]
- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#3 under sissid).
- Klitzing, Richard. "starp".
- Wikipedia Contributors. "Pentagrammic crossed antiprism".
- McCooey, David. "Pentagrammic Crossed Antiprism"