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

Overview

Group: SmallGroup(672,1254)
Rank: 3
Schläfli Type: {6,6}
Vertices, edges, …: 56, 168, 56
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

2-fold

{6,6}*336

Covers minimal covers in bold

2-fold

{6,6}*1344

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

29 facets

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

29 vertex figures

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

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

11 facets

8 of {6}*12
2 of {3}*6
1 of {2}*4

11 vertex figures

8 of {6}*12
2 of {3}*6
1 of {2}*4

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.