Quasidisprismatodishecatonicosachoron

Quasidisprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quadippady
Coxeter diagram	x5/3o3o5x ()
Elements
Cells	720 pentagonal prisms, 720 pentagrammic prisms, 120 dodecahedra, 120 great stellated dodecahedron
Faces	3600 squares, 1440 pentagons, 1440 pentagrams
Edges	7200 (as 3600 fissary)
Vertices	2400 (as 600 fissary)
Vertex figure	Compound of 4 triangular retroantipodiums, edge lengths (√5–1)/2 (small base), (1+√5)/2 (large base), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	${\frac {525}{2}}=262.5$
Dichoral angles	Gissid–5/2–stip: 162°
	Doe-5–pip: 54°
	Stip–4–pip: $\arccos \left({\frac {\sqrt {10+2{\sqrt {5}}}}{5}}\right)\approx 40.46123^{\circ }$
Related polytopes
Army	Hi
Regiment	Dattady
Conjugate	Quasidisprismatodishecatonicosachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Feral

The quasidisprismatodishecatonicosachoron, or quadippady, is a nonconvex fissary uniform polychoron that consists of 120 regular dodecahedra, 120 great stellated dodecahedra, 720 pentagonal prisms, and 720 pentagrammic prisms. 4 dodecahedra, 4 great stellated dodecahedra, 12 pentagonal prisms, and 12 pentagrammic prisms join at each vertex. It is the result of pushing the cells of either a grand hecatonicosachoron or a great stellated hecatonicosachoron inwards.

It is fissary as vertices coincide by four, producing a compound vertex figure; in addition, edges coincide by two.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the ditetrahedronary dishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 18: Ditetrahedrals" (#F15).

• Klitzing, Richard. "quadippady".