Polytope of Type {4,8} with group SmallGroup(672,1254)

Overview

Group: SmallGroup(672,1254)
Rank: 3
Schläfli Type: {4,8}
Vertices, edges, …: 42, 168, 84
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{4,8}*336a

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*(s1*s0*s2)^6*s1> of order 2

42 facets

42 of {4}*8

21 vertex figures

21 of {8}*16

Representations

Permutation Representation (GAP)

s0 := (3,7)(4,8)(5,6);;
s1 := ( 1, 3)( 2, 7)( 4, 5)( 9,10);;
s2 := (1,2)(3,4)(5,6)(7,8);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(10)!(3,7)(4,8)(5,6);
s1 := Sym(10)!( 1, 3)( 2, 7)( 4, 5)( 9,10);
s2 := Sym(10)!(1,2)(3,4)(5,6)(7,8);
poly := sub<Sym(10)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.