Small tritrigonary dishecatonicosihexacosichoron

Small tritrigonary dishecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Stutdahix
Elements
Cells	600 octahemioctahedra, 120 small ditrigonary icosidodecahedra, 120 small icosicosidodecahedra
Faces	2400+2400 triangles, 1440 pentagrams, 2400 hexagons
Edges	3600+7200
Vertices	2400
Vertex figure	Inverted triangular cupola, edge lengths 1 (top pseudo-triangle and one set of base edges), √5–1)/2 (remaining base edges), and √3 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {8+3{\sqrt {5}}}}\approx 3.83513$
Dichoral angles	Sidtid–3–oho: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Siid–6–oho: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Sidtid–5/2–siid: 144°
	Siid–3–oho: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Related polytopes
Army	Semi-uniform sidpixhi, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (dodecahedra), 1 (tetrahedra)
Regiment	Stut phiddix
Conjugate	Great tritrigonary dishecatonicosihexacosichoron
Abstract & topological properties
Flag count	144000
Euler characteristic	–600
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small tritrigonary dishecatonicosihexacosichoron, or stutdahix, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra, 600 octahemioctahedra, and 120 small icosicosidodecahedra. One small ditrigonary icosidodecahedron, three octahemioctahedra, and three small icosicosidodecahedra join at each vertex.

It is a blend of a small tritrigonary trishecatonicosihexacosichoron and a small tritrigonary dishexacosidishecatonicosachoron, blending out the tetrahedral cells.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small tritrigonary prismatohecatonicosidishexacosichoron.

External links

• Bowers, Jonathan. "Category 24: Stut Phiddix Regiment" (#1310).