Great disprismatoicositetricositetrachoron

Great disprismatoicositetricositetrachoron
Rank	4
Type	Semi-uniform
Space	Spherical
Notation
Coxeter diagram	a3b4c3d
Elements
Cells	96+96 ditrigonal prisms, 24+24 great rhombicuboctahedra
Faces	288+288+288 rectangles, 192+192 ditrigons, 144 ditetragons
Edges	576+576+576+576
Vertices	1152
Vertex figure	Irregular tetrahedron
Measures (edge lengths a, b, c, d)
Circumradius	$\sqrt{a^2+3b^2+3c^2+d^2+3ab+3cd+(2ac+ad+4bc+2bd)\sqrt2}$
Dichoral angles	Dittip–4–dittip: $\arccos\left(-\frac{2\sqrt2}{3}\right) ≈ 160.52878°$
	Girco–6–dittip: 150°
	Girco–4–dittip: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561°$
	Girco–8–girco: 135°
Central density	1
Related polytopes
Dual	Tetrahedral chiliahecatonpentacontadichoron
Conjugate	Great quasidisprismatoicsoitetricositetrachoron
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The great disprismatoicositetricositetrachoron is a convex semi-uniform polychoron that is a variant of the great prismatotetracontoctachoron with only regular icositetrachoric and not doubled icositetrachoric symmetry. As such it can be represented by a3b4c3d, and has 48 great rhombicuboctahedra of two types, forms c4b3a and b4c3d) and 192 ditrigonal prisms (two types, forms a c3d and d a3b) as cells, with 4 edge lengths. It is the most complex isogonal polytope generally possible with F4 symmetry.

It can generally be alternated into a snub icositetrachoron, which is also not uniform.