Polytope of Type {6,10} with group SmallGroup(1320,133)

Overview

Group: SmallGroup(1320,133)
Rank: 3
Schläfli Type: {6,10}
Vertices, edges, …: 66, 330, 110
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 1, 2)( 3, 7)( 4,12)( 5, 6)( 8,10)( 9,11);;
s1 := ( 1, 3)( 2, 8)( 4, 6)( 5, 9)( 7,11)(10,12);;
s2 := ( 1, 3)( 2, 7)( 4, 5)( 6,12)( 8,10);;
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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(12)!( 1, 2)( 3, 7)( 4,12)( 5, 6)( 8,10)( 9,11);
s1 := Sym(12)!( 1, 3)( 2, 8)( 4, 6)( 5, 9)( 7,11)(10,12);
s2 := Sym(12)!( 1, 3)( 2, 7)( 4, 5)( 6,12)( 8,10);
poly := sub<Sym(12)|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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;

References