Rank4
TypeUniform
Notation
Bowers style acronymDitdidap
Elements
Cells12 pentagonal antiprisms, 12 pentagrammic antiprisms, 2 ditrigonary dodecadodecahedra
Faces120 triangles, 24 pentagons, 24 pentagrams
Edges60+120
Vertices40
Vertex figureInverted retrotriangular cupola, edge lengths (5–1)/2, (1+5)/2 (3 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Dichoral anglesDitdid–5–pap: ${\displaystyle \arccos \left({\frac {{\sqrt {5}}-3}{2}}\right)\approx 112.45552^{\circ }}$
Ditdid–5/2–stap: 90°
Stap–3–pap: ${\displaystyle \arccos \left({\sqrt {\frac {3{\sqrt {5}}-5}{10}}}\right)\approx 65.58743^{\circ }}$
Height${\displaystyle {\sqrt {\frac {{\sqrt {5}}-1}{2}}}\approx 0.78615}$
Number of external pieces518
Level of complexity78
Related polytopes
ArmySemi-uniform Dope
RegimentSidtidap
DualMedial triambic icosahedral antitegum
Abstract & topological properties
Euler characteristic2
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The ditrigonary dodecadodecahedral antiprism is a nonconvex uniform polychoron that consists of 2 ditrigonary dodecadodecahedra, 12 pentagonal antiprisms, and 12 pentagrammic antiprisms. Each vertex joins 1 ditrigonary dodecadodecahedron, 3 pentagrammic antiprisms, and 3 pentagonal antiprisms.

The pentagonal antiprism cells pass through the center of the polychoron.

## Vertex coordinates

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