Icositetricositetrachoron

Icositetricositetrachoron
Rank	4
Type	Semi-uniform
Space	Spherical
Notation
Coxeter diagram	o3x4y3o
Elements
Cells	24+24 truncated cubes
Faces	96+96 triangles, 144 ditetragons
Edges	288+288
Vertices	288
Vertex figure	Digonal disphenoid
Measures (edge lengths a, b)
Circumradius	$\sqrt{3a^2+3b^2+4ab\sqrt2}$
Hypervolume	$29a^4+180a^2b^2+29b^4+(84a^3b+84ab^3)\sqrt2$
Dichoral angles	Tic–8–tic: 135°
	Tic–3–tic: 120°
Central density	1
Related polytopes
Dual	Disphenoidal diacosioctacontoctachoron
Conjugate	Great icositetricositetrachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The icositetricositetrachoron is a convex semi-uniform polychoron that is a variant of the tetracontoctachoron with only regular icositetrachoric and not doubled icositetrachoric symmetry. As such it can be represented by o3x4y3o and has 48 truncated cubes of two types (forms x4y3o and y4x3o), with two edge lengths.