Small pseudorhombic prismatotesseract

Small pseudorhombic prismatotesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Spript
Elements
Cells	32 triangular prisms, 24 octagonal prisms, 8 truncated cubes
Faces	64 triangles, 48+96 squares, 48 octagons
Edges	96+192
Vertices	96
Vertex figure	Isosceles triangular retroprism, edge lengths 1 (2), √2 (6), and √2+√2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Hypervolume	$22{\frac {3+2{\sqrt {2}}}{3}}\approx 42.74180$
Dichoral angles	Tic–3–trip: 90°
	Op–4–op: 90°
	Tic–8–op: 45°
	Trip–4–op: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Central density	1
Related polytopes
Army	Srit
Regiment	Srit
Conjugate	Great pseudorhombic prismatotesseract
Convex core	Tesseract
Abstract & topological properties
Flag count	4608
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The small pseudorhombic prismatotesseract, or spript, is a nonconvex uniform polychoron that consists of 8 truncated cubes, 32 triangular prisms, and 24 octagonal prisms. Two truncated cubes, two triangular prisms, and four octagonal prisms join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#143).

• Klitzing, Richard. "spript".