Polytope of Type {6,45} with group SmallGroup(1080,263)

Overview

Group: SmallGroup(1080,263)
Rank: 3
Schläfli Type: {6,45}
Vertices, edges, …: 12, 270, 90
Order of s₀s₁s₂: 45
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

3-fold

{6,15}*360

9-fold

{6,5}*120c

18-fold

{3,5}*60

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (11,12)(13,14);;
s1 := ( 2, 4)( 3, 6)( 5, 8)( 7, 9)(10,11)(13,14);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)(11,13)(12,14);;
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*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(14)!(11,12)(13,14);
s1 := Sym(14)!( 2, 4)( 3, 6)( 5, 8)( 7, 9)(10,11)(13,14);
s2 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)(11,13)(12,14);
poly := sub<Sym(14)|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*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;

References