Rectified great ditrigonary hexacosihecatonicosachoron

Rectified great ditrigonary hexacosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Riggidtixhi
Coxeter diagram	(o3x3o3/2o5*b)
Elements
Cells	600 octahedra, 120 great ditrigonary icosidodecahedra, 120 icosidodecahedra
Faces	2400+2400 triangles, 1440 pentagons
Edges	7200
Vertices	1200
Vertex figure	Tripod prism, base edge lengths 1 and (1+√5)/2, side edge length 1
Measures (edge length 1)
Circumradius	${\sqrt {3}}\approx 1.73205$
Hypervolume	$20\left(5+9{\sqrt {5}}\right)\approx 502.49224$
Dichoral angles	Gidtid–3–oct: $\arccos \left(-{\frac {\sqrt {10}}{4}}\right)\approx 142.23876^{\circ }$
	Gidtid–5–id: 108°
	Id–3–oct: $\arccos \left(-{\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 97.76124^{\circ }$
Central density	39
Related polytopes
Army	Rahi
Regiment	Rissidtixhi
Conjugate	Rectified small ditrigonary hexacosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–600
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The rectified great ditrigonary hexacosihecatonicosachoron, or riggidtixhi, is a nonconvex uniform polychoron that consists of 600 regular octahedra, 120 great ditrigonary icosidodecahedra, and 120 icosidodecahedra. 2 great ditrigonary icosidodecahedra, 3 icosidodecahedra, and 3 octahedra join at each tripod prismatic vertex. As the name suggests, it can be obtained by rectifying the great ditrigonary hexacosihecatonicosachoron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified small ditrigonary hexacosihecatonicosachoron.

Related polychora

Rissidtixhi regiment

Index	Name	OBSA	Company	Subcategory
1147	Rectified small ditrigonary hexacosihecatonicosachoron	Rissidtixhi	Rissidtixhi	Main nine
1148	Rectified ditrigonary dishecatonicosachoron	Ridtidohi	Ridtidohi	Main nine
1149	Rectified great ditrigonary hexacosihecatonicosachoron	Riggidtixhi	Riggidtixhi	Main nine
1150	Small ditrigonary dishecatonicosachoron	Sidditdy	Sidditdy	Main nine
1151	Retroditrigonary dishecatonicosachoron	Ridditdy	Ridditdy	Main nine
1152	Great ditrigonary dishecatonicosachoron	Gidditdy	Gidditdy	Main nine
1153	Ditrigonary hexacosidishecatonicosachoron	Dittixdy		Main nine
1154	Ditrigonary trishecatonicosachoron	Dittathi		Main nine
1155	Toroidal ditrigonary hexacosidishecatonicosachoron	Todtixady		Main nine
1156	Small ditrigonary dishecatonicosihecatonicosachoron	Sidtid hihy		Sixteen trapezics
1157	Ditrigonary hecatonicosidishecatonicosachoron	Dithidy		Sixteen trapezics

External links

• Bowers, Jonathan. "Category 23: Rissidtixhi Regiment" (#1149).

• Klitzing, Richard. "riggidtixhi".