Prismatoprismatohecatonicosachoron

Prismatoprismatohecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Paphi
Elements
Cells	1200 triangular prisms, 720 pentagonal prisms, 120 small dodecicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagons, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Inverted triangular antipodium, edge lengths 1 (top base), (1+√5)/2 (bottom base), √2 (side edges of triangles), and √(5+√5)/2 (side edges of crossed trapezoids)
Measures (edge length 1)
Circumradius	$3+{\sqrt {5}}\approx 5.23607$
Hypervolume	$140(25+11{\sqrt {5}})\approx 6943.54469$
Dichoral angles	Pip–4–trip: $\arccos \left(-{\sqrt {\frac {10+2{\sqrt {5}}}{15}}}\right)\approx 169.18768^{\circ }$
	Saddid–3–trip: 150°
	Saddid–10–saddid: 144°
	Saddid–5–pip: 18°
Number of external pieces	5880
Level of complexity	17
Related polytopes
Army	Sidpixhi
Regiment	Sidpixhi
Conjugate	Disprismatointercepted hecatonicosachoron
Abstract & topological properties
Euler characteristic	1320
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The prismatoprismatohecatonicosachoron, or paphi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 1200 triangular prisms, and 120 small dodecicosidodecahedra. Three pentagonal prisms, three triangular prisms, and three small dodecicosidodecahedra join at each vertex.

It also has 120 dodecahedra and 600 tetrahedra as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#458).