Small ditrigonal hecatonicosihexacosihecatonicosachoron

Small ditrigonal hecatonicosihexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidthixhi
Coxeter diagram	o3o3x5x5/3*b ()
Elements
Cells	600 tetrahedra, 120 great stellated dodecahedra, 120 small ditrigonal dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Crossed triangular frustum, edge lengths 1 (large base), (√5–1)/2 (small base), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {13-3{\sqrt {5}}}{2}}}\approx 1.77367$
Hypervolume	$5{\frac {412{\sqrt {5}}-685}{4}}\approx 295.32501$
Dichoral angles	Sidditdid–3–tet: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
	Sidditdid–10–sidditdid: 72°
	Sidditdid–5/2–gissid: 72°
Number of external pieces	51120
Level of complexity	214
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Sadixady
Conjugate	Great ditrigonal hecatonicosihexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

Not to be confused with sidtixhi.

The small ditrigonal hecatonicosihexacosihecatonicosachoron, or sidthixhi, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 great stellated dodecahedra, and 120 small ditrigonal dodecicosidodecahedra. 1 tetrahedron, 1 great stellated dodecahedron, and 3 small ditrigonal dodecicosidodecahedra join at each vertex.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#471).

• Klitzing, Richard. "sidthixhi".