Small trisoctachoron

Small trisoctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sto
Elements
Cells	8 tetrahedra, 8 truncated tetrahedra, 8 octahemioctahedra
Faces	32+32 triangles, 32 hexagons
Edges	48+48
Vertices	32
Vertex figure	Crossed triangular cuploid, edge lengths 1 (top triangle and base pseudo-triangle) and √3 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt6}{2} ≈ 1.22475$
Dichoral angles	Oho–3–tet: 120°
	Oho–6–tut: 120°
	Oho–3–tut: 60°
Number of external pieces	248
Level of complexity	36
Related polytopes
Army	Rit
Regiment	Rit
Conjugate	None
Abstract & topological properties
Euler characteristic	8
Orientable	No
Properties
Symmetry	D4, order 192
Convex	No
Nature	Tame

The small trisoctachoron, or sto, is a nonconvex uniform polychoron that consists of 8 tetrahedra, 8 octahemioctahedra, and 8 truncated tetrahedra. One tetrahedron, three octahemioctahedra, and three truncated tetrahedra join at each vertex.

It also has 8 tetrahedra as pseudofacets.

It is one of two members of the regiment of the rectified tesseract to have only half the symmetry, the other is the great trisoctachoron.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified tesseract.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#482).

• Klitzing, Richard. "sto".