Great spinoprismatodishecatonicosachoron

Great spinoprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gnappady
Elements
Cells	720 pentagrammic prisms, 120 great stellated dodecahedra, 120 great rhombidodecahedra
Faces	3600 squares, 1440 pentagrams, 720 decagrams
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular podic crown, edge lengths (√5–1)/2 (top triangle), √2 (side edges of triangles), and √(5–√5)/2 (edges between butterflies)
Measures (edge length 1)
Circumradius	$3-{\sqrt {5}}\approx 0.76393$
Dichoral angles	Gird–4–stip: $\arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }$
	Gird–10/3–gird: 108°
	Gissid–5/2–stip: 54°
Number of external pieces	372120
Level of complexity	1457
Related polytopes
Army	Sidpixhi
Regiment	Gixhihy
Conjugate	Small spinoprismatodishecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The great spinoprismatodishecatonicosachoron, or gnappady, is a nonconvex uniform polychoron that consists of 120 great rhombidodecahedra, 120 great stellated dodecahedra, and 720 pentagrammic prisms. Three great rhombidodecahedra, one great stellated dodecahedron, and three pentagrammic prisms join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great hexacosihecatonicosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#504).