Polytope of Type {6,8} with group SmallGroup(672,1254)

Overview

Group: SmallGroup(672,1254)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 42, 168, 56
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{6,8}*336b

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=<s1*s0*s1*s2*(s1*s0)^2*s2*s1*s2> of order 2

29 facets

27 of {6}*12
2 of {3}*6

21 vertex figures

21 of {8}*16

Representations

Permutation Representation (GAP)

s0 := ( 1, 2)( 3, 6)( 4, 8)( 5, 7)( 9,10);;
s1 := (2,3)(4,6)(5,7);;
s2 := (1,3)(2,6)(4,7)(5,8);;
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.