Great ditrigonary icosidodecahedral antiprism

The great ditrigonary icosidodecahedral antiprism or gidtidap, is a nonconvex uniform polychoron that consists of 2 great ditrigonary icosidodecahedra, 12 pentagonal antiprisms, and 40 tetrahedra. Each vertex joins 1 great ditrigonary icosidodecahedron, 3 pentagonal antiprisms, and 4 tetrahedra.

Great ditrigonary icosidodecahedral antiprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidtidap
Coxeter diagram
Elements
Cells	40 tetrahedra, 12 pentagonal antiprisms, 2 great ditrigonary icosidodecahedra
Faces	40+120 triangles, 24 pentagons
Edges	60+120
Vertices	40
Vertex figure	Retrotriangular cupola, edge lengths (1+√5)/2 (3 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{5+\sqrt5}{8}} ≈ 0.95106$
Hypervolume	0
Dichoral angles	Gidtid–3–tet: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124^\circ$
	Tet–3–pap: $\arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876^\circ$
	Gidtid–5–pap: $\arccos\left(\frac{3-\sqrt5}{2}\right) ≈ 67.54448^\circ$
Height	$\sqrt{\frac{\sqrt5-1}{2}} ≈ 0.78615$
Related polytopes
Army	Semi-uniform Dope
Regiment	Sidtidap
Dual	Great triambic icosahedral antitegum
Abstract & topological properties
Euler characteristic	–10
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The pentagonal antiprism cells pass through the center of the polychoron, making it a hemipolychoron.

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" (#968).

• Klitzing, Richard. "gidtidap".