Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymDitdid
Coxeter diagramx5/3o3o5*a ()
Schläfli symbol${\displaystyle \{5,6\}_4}$
Elements
Faces12 pentagons, 12 pentagrams
Edges60
Vertices20
Vertex figureTripod, edge lengths (5–1)/2 and (1+5)/2
Petrie polygons30 skew rhombi
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt3}{2} \approx 0.86603}$
Volume0
Dihedral angle${\displaystyle \arccos\left(\frac{\sqrt5}{5}\right) \approx 63.43495^\circ}$
Central density4
Number of external pieces192
Level of complexity11
Related polytopes
ArmyDoe
RegimentSidtid
DualMedial triambic icosahedron
Convex coreDodecahedron
Abstract & topological properties
Euler characteristic–16
Schläfli type{5,6}
OrientableYes
Genus9
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The ditrigonary dodecadodecahedron, or ditdid, is a quasiregular uniform polyhedron. It consists of 12 pentagons and 12 pentagrams, with three of each joining at a vertex.

It is a faceting of the small ditrigonary icosidodecahedron, using its 12 pentagrams along with 12 additional pentagons.

This polyhedron is abstractly regular, being a quotient of the order-6 pentagonal tiling. Among the non-regular uniform polytopes, it shares this property with the dodecadodecahedron. Its realization may also be considered regular if one also counts conjugacies as symmetries.

This polyhedron is the vertex figure of the ditrigonary dishecatonicosachoron.

## Vertex coordinates

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

## Related polyhedra

o5/3o3o5*a truncations
Name OBSA CD diagram Picture