# Small ditrigonal dodecicosidodecahedron

(Redirected from Sidditdid)
Small ditrigonal dodecicosidodecahedron
Rank3
TypeUniform
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${\displaystyle {\sqrt {\frac {17+3{\sqrt {5}}}{8}}}\approx 1.72149}$
Volume${\displaystyle 7{\frac {15+{\sqrt {5}}}{6}}\approx 20.10875}$
Dihedral angles3–10: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
5/2–10: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{4}}\right)\approx 63.43495^{\circ }}$
Central density4
Number of external pieces212
Level of complexity13
Related polytopes
ArmySemi-uniform Srid, edge lengths ${\displaystyle {\frac {{\sqrt {5}}-1}{2}}}$ (pentagons), 1 (triangles)
RegimentSiid
DualSmall ditrigonal dodecacronic hexecontahedron
ConjugateGreat ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
Flag orbits4
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