Hecatonicosintercepted ditrigonal hexacosidishecatonicosachoron

Hecatonicosintercepted ditrigonal hexacosidishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hind tixady
Elements
Cells	600 truncated tetrahedra, 120 great icosidodecahedra, 120 small ditrigonal dodecicosidodecahedra, 120 icosidodecatruncated icosidodecahedra
Faces	1200+2400 triangles, 1440 pentagrams, 2400 hexagons, 1440 decagons, 720 decagrams
Edges	3600+7200
Vertices	3600
Vertex figure	Windowed wedge, edge lengths 1 (3), (1+√5)/2 (2), √3 (4), √(5+√5)/2 (4), and √(5–√5)/2 (2)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {15+3{\sqrt {5}}}{2}}}\approx 3.29456$
Hypervolume	$5{\frac {3445+671{\sqrt {5}}}{4}}\approx 6181.75201$
Dichoral angles	Gid–3–tut: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Sidditdid–5/2–gid: 144°
	Sidditdid–10–idtid: 144°
	Sidditdid–3–sidditdid: 120°
	Idtid–10/3–idtid: 108°
	Idtid–6–tut: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Related polytopes
Army	Semi-uniform srix
Regiment	Swavixady
Conjugate	Hexacosihecatonicosintercepted ditrigonal dishecatonicosachoron
Abstract & topological properties
Euler characteristic	1440
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The hecatonicosintercepted ditrigonal hexacosidishecatonicosachoron, or hind tixady, is a nonconvex uniform polychoron that consists of 120 great icosidodecahedra, 120 small ditrigonal dodecicosidodecahedra, 600 truncated tetrahedra, and 120 icosidodecatruncated icosidodecahedra. One great icosidodecahedron, two small ditrigonal dodecicosidodecahedra, two truncated tetrahedra, and four icosidodecatruncated icosidodecahedra join at each vertex.

Vertex coordinates

The vertices are the same as those of the regiment colonel, the small sphenoverted hexacosidishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#262).