Compound of six pentagrammic retroprisms
|Compound of six pentagrammic retroprisms|
|Bowers style acronym||Gissed|
|Components||6 pentagrammic retroprisms|
|Faces||60 triangles, 12 pentagrams|
|Vertex figure||Crossed isosceles trapezoid, edge length 1, 1, 1, (√–1)/2|
|Measures (edge length 1)|
|Number of external pieces||1272|
|Level of complexity||83|
|Army||Semi-uniform Tid, edge lengths (triangles), (between dipentagons)|
|Dual||Compound of six pentagrammic concave antitegums|
|Conjugate||Compound of six pentagonal antiprisms|
|Convex core||Pentakis dodecahedron|
|Abstract & topological properties|
|Symmetry||H3, order 120|
The great inverted snub dodecahedron, gissed, or compound of six pentagrammic retroprisms is a uniform polyhedron compound. It consists of 60 triangles and 12 pentagrams, with one pentagram and three triangles joining at a vertex.
This compound can be formed by inscribing six pentagrammic retroprisms within a great icosahedron (each by removing one pair of opposite vertices) and then rotating each retroprism by 36° around its axis.
A double cover of this compound occurs as a special case of the great inverted disnub dodecahedron.
Vertex coordinates[edit | edit source]
The vertices of a great inverted snub dodecahedron of edge length 1 are given by all even permutations of:
[edit | edit source]
- Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#50).
- Klitzing, Richard. "gissed".
- Wikipedia contributors. "Compound of six pentagrammic crossed antiprisms".