# Great disrhombidodecahedron

The great disrhombidodecahedron, giddird, or compound of twelve pentagrammic prisms is a uniform polyhedron compound. It consists of 60 squares and 24 pentagrams, with two pentagrams and four squares joining at a vertex.

Great disrhombidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGiddird
Elements
Components12 pentagrammic prisms
Faces60 squares, 24 pentagrams
Edges60+120
Vertices60
Vertex figureCompound of two isosceles triangles, edge lengths (5–1)/2, 2, 2
Measures (edge length 1)
Circumradius$\sqrt{\frac{15-2\sqrt5}{20}} \approx 0.72553$ Volume$3\sqrt{25-10\sqrt5} \approx 4.87380$ Dihedral angles4–5/2: 90°
4–4: 36°
Central density24
Number of external pieces672
Level of complexity42
Related polytopes
ArmySrid
RegimentGiddird
DualCompound of twelve pentagrammic tegums
ConjugateDisrhombidodecahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count720
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

It can be formed by combining the two chiral forms of the great chirorhombidodecahedron, which results in vertices pairing up and two components joining per vertex.

Its quotient prismatic equivalent is the pentagrammic prismatic dodecadakoorthowedge, which is fourteen-dimensional.

## Vertex coordinates

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

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

plus all even permutations of:

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