Trirectified 4 ₂₁ polytope

Trirectified 421 polytope
Rank	8
Type	Uniform
Notation
Bowers style acronym	Torfy
Coxeter diagram	o3o3o3x3o3o3o *e3o ()
Elements
Zetta	17280 trirectified 7-simplices; 2160 trirectified 7-cubes; 240 birectified 321 polytopes;
Exa	69120+138240+138240 birectified 6-simplices; 30240 birectified 6-orthoplexes; 6720 rectified 221 polytopes;
Peta	483840+483840 rectified 5-simplices; 60480 5-demicubes; 483840+967680 birectified 5-simplices; 181440 rectified 5-orthoplexes;
Tera	483840+967680 pentachora; 604800 hexadecachora; 1451520+2903040+2903040 rectified pentachora;
Cells	2419200+2419200+4838400 tetrahedra; 7257600 octahedra;
Faces	4838400+9676800 triangles
Edges	4838400
Vertices	241920
Vertex figure	Tetrahedral-rectified pentachoric duoprism, edge length 1
Measures (edge length 1)
Circumradius
Hypervolume
Dizettal angles	He–bril–sez:
	Sez–bril–sez:
	Branq–bril–he:
	Branq–brag–sez: 135°
	Branq–rojak–branq: 120°
Central density	1
Number of external pieces	19680
Level of complexity	105
Related polytopes
Army	Torfy
Regiment	Torfy
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E8, order 696729600
Convex	Yes
Nature	Tame

The trirectified 4₂₁ polytope, also called the trirectified dischiliahecatonhexaconta-myriaheptachiliadiacosioctaconta-zetton, is a convex uniform 8-polytope. It has 240 birectified 3₂₁ polytopes, 2160 trirectified 7-cubes, and 17280 trirectified 7-simplices as facets. 4 birectified 3₂₁ polytopes, 5 trirectified 7-cubes, and 5 trirectified 7-simplices join at each tetrahedral-rectified pentachoric duoprismatic vertex. As the name suggests, it is the trirectification of the 4₂₁ polytope.