1 ₄₂ polytope

1 42 polytope
Rank	8
Type	Uniform
Notation
Bowers style acronym	Bif
Coxeter diagram	o3o3o3o3o3o3o *e3x ()
Elements
Zetta	2160 7-demicubes; 240 132 polytopes;
Exa	69120 6-simplices; 30240 6-demicubes; 6720 122 polytopes;
Peta	483840 5-simplices; 60480+181440 5-demicubes;
Tera	241920+1451520 pentachora; 604800 hexadecachora;
Cells	1209600+2419200 tetrahedra
Faces	2419200 triangles
Edges	483840
Vertices	17280
Vertex figure	Birectified octaexon, edge length 1
Measures (edge length 1)
Circumradius	2
Hypervolume
Dizettal angles	Hesa–hop–hesa:
	Lin–hax–hesa: 135°
	Lin–mo–lin: 120°
Central density	1
Number of external pieces	2400
Level of complexity	15
Related polytopes
Army	Bif
Regiment	Bif
Conjugate	None
Abstract & topological properties
Flag count	10450944000
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E8, order 696729600
Flag orbits	15
Convex	Yes
Nature	Tame

The 1₄₂ polytope, also known as the diacositetraconta-dischiliahecatonhexaconta-zetton (abbreviated as 240-2160-zetton) or bif, is a convex uniform 8-polytope. It consists of 2160 7-demicubes and 240 1₃₂ polytopes}}, with 8 of each joining at each vertex forming a birectified 7-simplex as the vertex figure.

The diacositetraconta-dischiliahecatonhexaconta-zetton contains the vertices and edges of an inscribed stericated 8-orthoplex and pentic 8-cube.

Vertex coordinates[edit | edit source]

Coordinates for a diacositetraconta-dischiliahecatonhexaconta-zetton of edge length 1 are given by all permutations of

$\left(\pm {\sqrt {2}},\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0\right)$ ,

all permutations and even sign changes of

$\left({\frac {5{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$ ,

and all permutations and odd sign changes of

$\left({\frac {3{\sqrt {2}}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {3{\sqrt {2}}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$ ,
$\left({\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}},\,{\frac {\sqrt {2}}{2}}\right)$ .