# 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$\sqrt{\frac{17+3\sqrt5}{8}} \approx 1.72149$ Volume$7\frac{15+\sqrt5}{6} \approx 20.10875$ Dihedral angles3–10: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 100.81232^\circ$ 5/2–10: $\arccos\left(\frac{\sqrt5}{4}\right) \approx 63.43495^\circ$ Central density4
Number of pieces212
Level of complexity13
Related polytopes
ArmySemi-uniform Srid
RegimentSiid
DualSmall ditrigonal dodecacronic hexecontahedron
ConjugateGreat ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract properties
Euler characteristic–16
Topological properties
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
Ditrigonary dodecadodecahedron ditdid   Small complex icosidodecahedron (degenerate, ike+gad) cid   Great complex icosidodecahedron (degenerate, sissid+gike) gacid   Icosidodecadodecahedron ided   Small ditrigonal dodecicosidodecahedron sidditdid   Great ditrigonal dodecicosidodecahedron gidditdid   Icosidodecatruncated icosidodecahedron idtid   Snub icosidodecadodecahedron sided   