Polytope of Type {4,12,6} with group SmallGroup(1920,240505)

Overview

Group: SmallGroup(1920,240505)
Rank: 4
Schläfli Type: {4,12,6}
Vertices, edges, …: 4, 80, 120, 20
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{2,6,6}*480b

8-fold

{2,6,6}*240

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (1,8)(2,4)(3,5)(6,7);;
s1 := ( 1, 4)( 2, 7)( 3, 8)( 5, 6)(10,13)(11,12);;
s2 := ( 2, 4)( 3, 5)( 9,11);;
s3 := (10,11)(12,13);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(13)!(1,8)(2,4)(3,5)(6,7);
s1 := Sym(13)!( 1, 4)( 2, 7)( 3, 8)( 5, 6)(10,13)(11,12);
s2 := Sym(13)!( 2, 4)( 3, 5)( 9,11);
s3 := Sym(13)!(10,11)(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3 >;

References