# Compound of ten hexagonal prisms

The rhombisnub icosahedron, rosi, or compound of ten hexagonal prisms is a uniform polyhedron compound. It consists of 60 squares and 20 hexagons, with one hexagon and two squares joining at a vertex.

Compound of ten hexagonal prisms
Rank3
TypeUniform
Notation
Bowers style acronymRosi
Elements
Components10 hexagonal prisms
Faces60 squares, 20 hexagons
Edges60+60+60
Vertices120
Vertex figureIsosceles triangle, edge length 3, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5}}{2}}\approx 1.11803}$
Volume${\displaystyle 15{\sqrt {3}}\approx 25.98076}$
Dihedral angles4–4: 120°
4–6: 90°
Central density10
Number of external pieces1260
Level of complexity87
Related polytopes
ArmySemi-uniform Grid, edge lengths ${\displaystyle {\frac {-3+{\sqrt {3}}+{\sqrt {15}}}{6}}}$ (dipentagon-ditrigon), ${\displaystyle {\frac {-3-2{\sqrt {3}}+3{\sqrt {5}}}{6}}}$ (dipentagon-rectangle), ${\displaystyle {\frac {3-{\sqrt {3}}}{3}}}$ (ditrigon-rectangle)
RegimentRosi
DualCompound of ten hexagonal tegums
ConjugateCompound of ten hexagonal prisms
Convex coreIcosahedron
Abstract & topological properties
Flag count720
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

Its quotient prismatic equivalent is the ditrigonal trapezoprismatic decayottoorthowedge, which is twelve-dimensional.

## Vertex coordinates

The vertices of a rhombisnub icosahedron of edge length 1 are given by all even permutations of:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3+{\sqrt {3}}+3{\sqrt {5}}-{\sqrt {15}}}{12}},\,\pm {\frac {-3+{\sqrt {3}}+3{\sqrt {5}}+{\sqrt {15}}}{12}}\right)}$ ,
• ${\displaystyle \left(\pm 1,\,\pm {\frac {{\sqrt {15}}-{\sqrt {3}}}{12}},\,\pm {\frac {{\sqrt {3}}+{\sqrt {15}}}{12}}\right)}$ ,
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {3}}}{6}},\,\pm {\frac {3-2{\sqrt {3}}+3{\sqrt {5}}}{12}},\,\pm {\frac {-3+2{\sqrt {3}}+3{\sqrt {5}}}{12}}\right)}$ ,
• ${\displaystyle \left(\pm {\frac {3+{\sqrt {3}}-3{\sqrt {5}}+{\sqrt {15}}}{12}},\,\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {3}}+3{\sqrt {5}}+{\sqrt {15}}}{12}}\right)}$ ,
• ${\displaystyle \left(\pm {\frac {-3-2{\sqrt {3}}+3{\sqrt {5}}}{12}},\,\pm {\frac {3-{\sqrt {3}}}{6}},\,\pm {\frac {3+2{\sqrt {3}}+3{\sqrt {5}}}{12}}\right)}$ .