# Compound of six decagrammic prisms

Compound of six decagrammic prisms
Rank3
TypeUniform
Notation
Bowers style acronymGrassid
Elements
Components6 decagrammic prisms
Faces60 squares, 12 decagrams
Edges60+60+60
Vertices120
Vertex figureIsosceles triangle, edge length (5–5)/2, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {7-2{\sqrt {5}}}}{2}}\approx 0.79496}$
Volume${\displaystyle 15{\sqrt {5-2{\sqrt {5}}}}\approx 10.89814}$
Dihedral angles4–10/3: 90°
4–4: 72°
Central density18
Number of external pieces720
Level of complexity54
Related polytopes
ArmySemi-uniform Grid, edge lengths ${\displaystyle {\frac {-3+{\sqrt {5}}+{\sqrt {\frac {10+2{\sqrt {5}}}{5}}}}{2}}}$ (sipentagon-ditrigon), ${\displaystyle {\frac {3-{\sqrt {5}}}{2}}}$ (dipentagon-rectangle), ${\displaystyle {\frac {{\sqrt {5}}-1+{\sqrt {\frac {10-2{\sqrt {5}}}{5}}}}{2}}}$ (ditrigon-rectangle)
RegimentGrassid
DualCompound of six decagrammic tegums
ConjugateCompound of six decagonal prisms
Convex coreDeltoidal hexecontahedron
Abstract & topological properties
Flag count720
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great rhombisnub dodecahedron, grassid, or compound of six decagrammic prisms is a uniform polyhedron compound. It consists of 60 squares and 12 decagrams, with one decagon and two squares joining at a vertex.

## Vertex coordinates

Coordinates for the vertices of a great rhombisnub dodecahedron of edge length 1 are given by all even permutations of:

• ${\displaystyle \left(\pm {\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{40}}}\right),}$
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}+{\sqrt {\frac {10+2{\sqrt {5}}}{5}}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1-{\sqrt {5}}-{\sqrt {\frac {10-2{\sqrt {5}}}{5}}}}{4}}\right),}$
• ${\displaystyle \left(\pm {\frac {1-{\sqrt {5}}+{\sqrt {\frac {10+2{\sqrt {5}}}{5}}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {1-{\sqrt {5}}-{\sqrt {\frac {10+2{\sqrt {5}}}{5}}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {\frac {5-{\sqrt {5}}}{10}}}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {3-{\sqrt {5}}-{\sqrt {\frac {10+2{\sqrt {5}}}{5}}}}{4}},\,\pm {\frac {1}{2}},\,\pm {\frac {1-{\sqrt {5}}+{\sqrt {\frac {10-2{\sqrt {5}}}{5}}}}{4}}\right).}$