Small spinoprismatodishecatonicosachoron

Small spinoprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Snappady
Elements
Cells	720 pentagonal prisms, 120 dodecahedra, 120 small rhombidodecahedra
Faces	3600 squares, 1440 pentagons, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular crown, edge lengths (1+√5)/2 (top triangle), √2 (side edges of triangles), and √(5+√5)/2 (edges between butterflies)
Measures (edge length 1)
Circumradius	$3+{\sqrt {5}}\approx 5.23607$
Dichoral angles	Doe–5–pip: 162°
	Sird–4–pip: $\arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }$
	Sird–10–sird: 144°
Number of external pieces	4440
Level of complexity	13
Related polytopes
Army	Sidpixhi
Regiment	Sidpixhi
Conjugate	Great spinoprismatodishecatonicosachoron
Abstract & topological properties
Flag count	115200
Euler characteristic	0
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small spinoprismatodishecatonicosachoron, or snappady, is a nonconvex uniform polychoron that consists of 120 dodecahedra, 720 pentagonal prisms, and 120 small rhombidodecahedra. One dodecahedron, three pentagonal prisms, and three small rhombidodecahedra join at each vertex.

Gallery

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small disprismatohexacosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#460).