Pentapentachoron

Pentapentachoron
Rank	4
Type	Semi-uniform
Notation
Bowers style acronym	Pup
Coxeter diagram	o3x3y3o
Elements
Cells	5+5 truncated tetrahedra
Faces	10+10 triangles, 20 ditrigons
Edges	30+30
Vertices	30
Vertex figure	Digonal disphenoid
Measures (edge lengths a, b)
Circumradius	${\sqrt {\frac {3a^{2}+3b^{2}+4ab}{5}}}$
Hypervolume	$(11a^{4}+56a^{3}b+96a^{2}b^{2}+56ab^{3}+11a^{4}){\frac {\sqrt {5}}{96}}$
Dichoral angles	Tut–6–tut: $\arccos \left(-{\frac {1}{4}}\right)\approx 104.47751^{\circ }$
	Tut–3–tut: $\arccos \left({\frac {1}{4}}\right)\approx 75.52248^{\circ }$
Central density	1
Related polytopes
Dual	Disphenoidal triacontachoron
Conjugate	Pentapentachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The pentapentachoron is a convex semi-uniform polychoron that is a variant of the decachoron with only regular pentachoric and not doubled pentachoric symmetry. As such it can be represented by o3x3y3o and has 10 truncated tetrahedra (of two types (forms x3y3o and y3x3o), with two edge lengths.