# Small ditrigonal dodecicosidodecahedron

Small ditrigonal dodecicosidodecahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSidditdid
Coxeter diagramx5/3o3x5*a ()
Elements
Faces20 triangles, 12 pentagrams, 12 decagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, (5+5)/2, (5–1)/2, (5+5)/2
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{17+3\sqrt5}{8}} \approx 1.72149}$
Volume${\displaystyle 7\frac{15+\sqrt5}{6} \approx 20.10875}$
Dihedral angles3–10: ${\displaystyle \arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 100.81232^\circ}$
5/2–10: ${\displaystyle \arccos\left(\frac{\sqrt5}{4}\right) \approx 63.43495^\circ}$
Central density4
Number of external pieces212
Level of complexity13
Related polytopes
ArmySemi-uniform Srid
RegimentSiid
DualSmall ditrigonal dodecacronic hexecontahedron
ConjugateGreat ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The small ditrigonal dodecicosidodecahedron, or sidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagons. One triangle, one pentagram, and two decagons join at each vertex.

It is a faceting of the small icosicosidodecahedron, using its 12 pentagrams and 20 triangles along with 12 additional decagons.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedron.

## Related polyhedra

o5/3o3o5*a truncations
Name OBSA CD diagram Picture
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid