The great chirorhombidodecahedron, gikrid, or compound of six pentagrammic prisms is a uniform polyhedron compound. It consists of 30 squares and 12 pentagrams, with one pentagram and two squares joining at a vertex.
|Bowers style acronym||Gikrid|
|Components||6 pentagrammic prisms|
|Faces||30 squares, 12 pentagrams|
|Vertex figure||Isosceles triangle, edge lengths (√5–1)/2, √2, √2|
|Measures (edge length 1)|
|Dihedral angles||4–5/2: 90°|
|Number of external pieces||192|
|Level of complexity||38|
|Dual||Compound of six pentagrammic tegums|
|Convex core||Rhombic triacontahedron|
|Abstract & topological properties|
|Symmetry||H3+, order 60|
Its quotient prismatic equivalent is the pentagrammic prismatic hexateroorthowedge, which is eight-dimensional.
The vertices of a great chirorhombidodecahedron of edge length 1 are given by all permutations of:
plus all even permutations of:
This compound is chiral. The compound of the two enantiomorphs is the great disrhombidodecahedron.
- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#42).
- Klitzing, Richard. "gikrid".
- Wikipedia Contributors. "Compound of six pentagrammic prisms".