Great disprismatopentapentachoron

Great disprismatopentapentachoron
Rank	4
Type	Semi-uniform
Notation
Coxeter diagram	a3b3c3d
Elements
Cells	10+10 ditrigonal prisms, 5+5 great rhombitetratetrahedra
Faces	30+30+30 rectangles, 20+20+20 ditrigons
Edges	60+60+60+60
Vertices	120
Vertex figure	Irregular tetrahedron
Measures (edge lengths a, b, c, d)
Circumradius	${\sqrt {\frac {2a^{2}+3b^{2}+3c^{2}+2d^{2}+3ab+2ac+ad+4bc+2bd+3cd}{5}}}$
Dichoral angles	Dittip–4–dittip: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Gratet–6–dittip: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Gratet–4–dittip: $\arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }$
	Gratet–6–gratet: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
Central density	1
Related polytopes
Dual	Tetrahedral hecatonicosachoron
Conjugate	Great disprismatopentapentachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The great disprismatopentapentachoron is a convex semi-uniform polychoron that is a variant of the great prismatodecachoron with only regular pentachoric and not doubled pentachoric symmetry. As such it can be represented by a3b3c3d, and has 10 great rhombitetratetrahedra (of two types, forms a3b3c and b3c3d) and 20 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 A4 symmetry.

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