Ditrigonary dodecadodecahedral antiprism

Ditrigonary dodecadodecahedral antiprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ditdidap
Elements
Cells	12 pentagonal antiprisms, 12 pentagrammic antiprisms, 2 ditrigonary dodecadodecahedra
Faces	120 triangles, 24 pentagons, 24 pentagrams
Edges	60+120
Vertices	40
Vertex figure	Inverted retrotriangular cupola, edge lengths (√5–1)/2, (1+√5)/2 (3 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106$
Dichoral angles	Ditdid–5–pap: $\arccos \left({\frac {{\sqrt {5}}-3}{2}}\right)\approx 112.45552^{\circ }$
	Ditdid–5/2–stap: 90°
	Stap–3–pap: $\arccos \left({\sqrt {\frac {3{\sqrt {5}}-5}{10}}}\right)\approx 65.58743^{\circ }$
Height	${\sqrt {\frac {{\sqrt {5}}-1}{2}}}\approx 0.78615$
Number of external pieces	518
Level of complexity	78
Related polytopes
Army	Semi-uniform Dope
Regiment	Sidtidap
Dual	Medial triambic icosahedral antitegum
Abstract & topological properties
Euler characteristic	2
Orientable	No
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

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.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 20: Miscellaneous" (#967).

• Klitzing, Richard. "ditdidap".