Prismatorhombisnub icositetrachoron

Prismatorhombisnub icositetrachoron
(OFF file)
Rank	4
Type	Scaliform
Notation
Bowers style acronym	Prissi
Coxeter diagram	s3s4o3x ()
Elements
Cells	96 triangular cupolas 96 triangular prisms 24 truncated tetrahedra 24 icosahedra
Faces	96+192+288 triangles 288 squares 96 hexagons
Edges	144+288+576
Vertices	288
Vertex figure	Digonal-pentagonal wedge, pentagon edge length 1, other lateral edge lengths 1, √2, and √3
Measures (edge length 1)
Circumradius	${\sqrt {4+{\sqrt {5}}}}\approx 2.49721$
Hypervolume	${\frac {309+140{\sqrt {5}}}{4}}\approx 155.51238$
Dichoral angles	Trip–4–tricu: $\arccos \left(-{\frac {\sqrt {30}}{6}}\right)\approx 155.90516^{\circ }$
	Tut–3–tricu: $\arccos \left({\frac {1-3{\sqrt {5}}}{8}}\right)\approx 135.52249^{\circ }$
	Tut–6–tricu: $\arccos \left(-{\frac {1+3{\sqrt {5}}}{8}}\right)\approx 164.47751^{\circ }$
	Ike–3–trip: 150°
	Ike–3–tricu: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
Central density	1
Related polytopes
Army	Prissi
Regiment	Prissi
Dual	Dipentanotched diacosioctacontoctachoron
Conjugate	Prismatorhombiretrosnub icositetrachoron
Abstract & topological properties
Flag count	13824
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4/2, order 576
Flag orbits	24
Convex	Yes
Nature	Tame

The prismatorhombisnub icositetrachoron (OBSA: prissi) is a convex scaliform polychoron. It consists of 96 triangular prisms, 96 triangular cupolas, 24 truncated tetrahedra, and 24 icosahedra. 1 icosahedron, 1 truncated tetrahedron, 2 triangular prisms, and 3 triangular cupolas join at each vertex.

It can be constructed from the snub disicositetrachoron by expanding the icosahedral cells outward by unit distance, or from the prismatorhombated icositetrachoron by alternating the triangles and equalizing edge lengths. It is also a subsymmetrical faceting of the prismatodishecatonicosachoron.

It contains the vertices of a pyritosnub tesseract with regular icosahedra and uniform triangular prisms.

Vertex coordinates

A prismatorhombisnub icositetrachoron of edge length 1 has vertex coordinates given by all even permutations of:

• $\left(0,\pm {\frac {1}{2}},\pm {\frac {1+{\sqrt {5}}}{4}},\pm {\frac {7+{\sqrt {5}}}{4}}\right)$,
• $\left(\pm {\frac {1}{2}},\pm 1,\pm {\frac {3+{\sqrt {5}}}{4}},\pm {\frac {5+{\sqrt {5}}}{4}}\right)$.

Representations

A prismatorhombisnub icositetrachoron has the following Coxeter diagrams:

• s3s4o3x () (full symmetry)
• fox3xxx3xfo *b3oxf&#zx (D4 symmetry)

External links

• Bowers, Jonathan. "Category S3: Special Scaliforms" (#S30).

• Klitzing, Richard. "prissi".
• Quickfur. "The Runcinated Snub 24-cell".

• Hi.gher.Space Wiki Contributors. "Runcinated snub demitesseract".

• Wikipedia contributors. "Runcic snub 24-cell".