Small spinoprismatohexacosihecatonicosachoron

Small spinoprismatohexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Snapaxhi
Elements
Cells	600 tetrahedra, 1200 triangular prisms, 120 small rhombidodecahedra
Faces	2400 triangles, 3600 squares, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular crown, edge lengths 1 (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	Tet–3–trip: $\arccos \left(-{\frac {{\sqrt {6}}+{\sqrt {30}}}{8}}\right)\approx 172.23876^{\circ }$
	Sird–10–sird: 144°
	Sird–4–trip: $\arccos \left({\frac {{\sqrt {3}}+{\sqrt {15}}}{6}}\right)\approx 20.90516^{\circ }$
Number of external pieces	5520
Level of complexity	14
Related polytopes
Army	Sidpixhi
Regiment	Sidpixhi
Conjugate	Great spinoprismatohexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	0
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small spinoprismatohexacosihecatonicosachoron, or snapaxhi, is a nonconvex uniform polychoron that consists of 600 tetrahedra, 1200 triangular prisms, and 120 small rhombidodecahedra. One tetrahedron, three triangular 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" (#459).