Small disprismatoicositetricositetrachoron

Small disprismatoicositetricositetrachoron
Rank	4
Type	Semi-uniform
Notation
Coxeter diagram	x3o4o3y
Elements
Cells	24+24 octahedra, 96+96 triangular prisms
Faces	192+192 triangles, 288 rectangles
Edges	288+288
Vertices	144
Vertex figure	Square antipodium
Measures (edge lengths a, b)
Circumradius	${\sqrt {a^{2}+b^{2}+ab}}$
Hypervolume	$2a^{4}+18a^{2}b^{2}+2b^{4}+(8a^{3}b+8ab^{3}){\sqrt {2}}$
Dichoral angles	Trip–4–trip: $\arccos \left(-{\frac {2{\sqrt {2}}}{3}}\right)\approx 160.52878^{\circ }$
	Oct–3–trip: 150°
Central density	1
Related polytopes
Dual	Tetragonal-trapezohedral hecatontetracontatetrachoron
Conjugate	Quasidisprismatoicositetricositetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The small disprismatoicositetricositetrachoron is a convex semi-uniform polychoron that is a variant of the small prismatotetracontoctachoron with only regular icositetrachoric and not doubled icositetrachoric symmetry. As such it can be represented by x3o4o3y, and has 48 octahedra (of two types, sizes x and y) and 192 triangular prisms (two types, forms x y3o and y x3o) as cells, with two edge lengths.