Prismatohemidecachoron

Prismatohemidecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Phud
Elements
Cells	20 triangular prisms, 5 octahemioctahedra
Faces	40 triangles, 30 squares, 10 hexagons
Edges	60
Vertices	20
Vertex figure	Inverted triangular antiprism, edge lengths 1 (bas edges), √2 (side edges of triangles), and √3 (side edges of bowties)
Edge figure	trip 4 trip 4 trip 3 oho 6 oho 3
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {5{\sqrt {5}}}{8}}\approx 1.39754$
Dichoral angles	Trip–4–trip: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Oho–6–oho: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Oho–3–trip: $\arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }$
Number of external pieces	60
Level of complexity	7
Related polytopes
Army	Spid
Regiment	Spid
Conjugate	None
Abstract & topological properties
Flag count	1200
Euler characteristic	15
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	No
Nature	Wild

The prismatohemidecachoron, or phud, is a nonconvex uniform polychoron that consists of 20 triangular prisms and 5 octahemioctahedra. Six triangular prisms and three octahemioctahedra join at each vertex.

It also has 10 tetrahedra as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#445).

• Klitzing, Richard. "phud".