# Compound of twenty triangular prisms

(Redirected from Disrhombicosahedron)
Compound of twenty triangular prisms
Rank3
TypeUniform
Notation
Bowers style acronymDri
Elements
Components20 triangular prisms
Faces40 triangles as 20 hexagrams, 60 squares
Edges60+120
Vertices60
Vertex figureCompound of two isosceles triangle, edge lengths 1, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {21}}{6}}\approx 0.76376}$
Volume${\displaystyle 5{\sqrt {3}}\approx 8.66025}$
Dihedral angles4–3: 90°
4–4: 60°
Central density20
Number of external pieces1140
Level of complexity60
Related polytopes
ArmySemi-uniform Ti, edge lengths ${\displaystyle {\frac {{\sqrt {15}}-{\sqrt {3}}}{6}}}$ (pentagons), ${\displaystyle {\frac {3{\sqrt {3}}-{\sqrt {15}}}{6}}}$ (between ditrigons)
RegimentDri
DualCompound of twenty triangular tegums
ConjugateCompound of twenty triangular prisms
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count720
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The disrhombicosahedron, dri, or compound of twenty triangular prisms is a uniform polyhedron compound. It consists of 60 squares and 40 triangles (pairs of which are in the same plane, combining to 20 hexagrams), with two triangles and four squares joining at a vertex.

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

Its quotient prismatic equivalent is the triangular prismatic icosayodakoorthowedge, which is 22-dimensional.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\frac {\sqrt {15}}{6}},\,\pm {\frac {\sqrt {3}}{6}},\,\pm {\frac {\sqrt {3}}{6}}\right),}$

plus all even permutations of:

• ${\displaystyle \left(0,\,\pm {\frac {3{\sqrt {3}}+{\sqrt {15}}}{12}},\,\pm {\frac {3{\sqrt {3}}-{\sqrt {15}}}{12}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {3}}{3}},\,\pm {\frac {{\sqrt {15}}-{\sqrt {3}}}{12}},\,\pm {\frac {{\sqrt {3}}+{\sqrt {15}}}{12}}\right).}$