Great chirorhombidodecahedron

Great chirorhombidodecahedron
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gikrid
Elements
Components	6 pentagrammic prisms
Faces	30 squares, 12 pentagrams
Edges	30+60
Vertices	60
Vertex figure	Isosceles triangle, edge lengths (√5–1)/2, √2, √2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{15-2\sqrt5}{20}} ≈ 0.72553$
Volume	$\frac{3\sqrt{25-10\sqrt5}}{2} ≈ 2.43690$
Dihedral angles	4–5/2: 90°
	4–4: 36°
Central density	12
Related polytopes
Army	Srid
Regiment	Gikrid
Dual	Compound of six pentagrammic tegums
Conjugate	Chirorhombidodecahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3+, order 60
Convex	No
Nature	Tame

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.

Its quotient prismatic equivalent is the pentagrammic prismatic hexateroorthowedge, which is eight-dimensional.

Vertex coordinates

The vertices of a great chirorhombidodecahedron of edge length 1 are given by all permutations of:

• $\left(±\sqrt{\frac{5+2\sqrt5}{20}},\,±\sqrt{\frac{5-2\sqrt5}{20}},\,±\sqrt{\frac{5-2\sqrt5}{20}}\right),$

plus all even permutations of:

• $\left(0,\,±\sqrt{\frac{5+\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{8}}\right),$
• $\left(±\sqrt{\frac{5+\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{40}},\,±\sqrt{\frac{5-\sqrt5}{10}}\right).$

This compound is chiral. The compound of the two enantiomorphs is the great disrhombidodecahedron.

External links

• Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#42).

• Klitzing, Richard. "gikrid".

• Wikipedia Contributors. "Compound of six pentagrammic prisms".