Small rhombic dispentachoron

Small rhombic dispentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirdop
Coxeter diagram
Elements
Cells	10 triangular prisms, 5 truncated tetrahedra, 5 cubohemioctahedra
Faces	20 triangles, 30 squares, 20 hexagons
Edges	30+60
Vertices	30
Vertex figure	Butterfly wedge, edge lengths 1 (bases), √2 (sides of outer triangles), and √3 (sides of inner triangles)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {35}}{5}}\approx 1.18322$
Dichoral angles	Cho–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }$
	Cho–6–tut: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Tut–3–trip: $\arccos \left({\frac {\sqrt {6}}{4}}\right)\approx 52.23876^{\circ }$
Related polytopes
Army	Srip
Regiment	Srip
Conjugate	None
Convex core	Pentachoron
Abstract & topological properties
Flag count	1200
Euler characteristic	–10
Orientable	No
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

The small rhombic dispentachoron, or sirdop, is a nonconvex uniform polychoron that consists of 5 truncated tetrahedra, 5 cubohemioctahedra, and 10 triangular prisms. 2 of each type of cell join at each vertex.

Cross-sections

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small rhombated pentachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#135).

• Klitzing, Richard. "sirdop".