Small disprismatopentapentachoron

Small disprismatopentapentachoron
Rank	4
Type	Semi-uniform
Notation
Coxeter diagram	x3o3o3y
Elements
Cells	5+5 tetrahedra, 10+10 triangular prisms
Faces	20+20 triangles, 30 rectangles
Edges	30+30
Vertices	20
Vertex figure	Triangular antipodium
Measures (edge lengths a, b)
Circumradius	${\sqrt {\frac {2a^{2}+2b^{2}+ab}{5}}}$
Hypervolume	$(a^{4}+16a^{3}b+36a^{2}b^{2}+16ab^{3}+b^{4}){\frac {\sqrt {5}}{96}}$
Dichoral angles	Trip–4–trip: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Tet–3–trip: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
Central density	1
Related polytopes
Dual	Trigonal-trapezohedral icosachoron
Conjugate	Small disprismatopentapentachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The small disprismatopentapentachoron is a convex semi-uniform polychoron that is a variant of the small prismatodecachoron with only regular pentachoric and not doubled pentachoric symmetry. As such it can be represented by x3o3o3y, and has 10 tetrahedra (of two types, sizes x and y) and 20 triangular prisms (two types, forms x y3o and y x3o) as cells, with two edge lengths.