Polytope of Type {4,5,3} with group SmallGroup(1920,240993)

Overview

Group: SmallGroup(1920,240993)
Rank: 4
Schläfli Type: {4,5,3}
Vertices, edges, …: 32, 160, 120, 16
Order of s₀s₁s₂s₃: 6
Order of s₀s₁s₂s₃s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Universal
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 := ( 2,11)( 3,10)( 5,16)( 6,14)( 7,13)( 8,15);;
s1 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(13,14)(15,16);;
s2 := ( 2, 5)( 3, 6)( 8,15)( 9,12)(10,14)(11,16);;
s3 := ( 1,12)( 2,11)( 5, 8)( 6, 7)(13,14)(15,16);;
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, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(16)!( 2,11)( 3,10)( 5,16)( 6,14)( 7,13)( 8,15);
s1 := Sym(16)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(13,14)(15,16);
s2 := Sym(16)!( 2, 5)( 3, 6)( 8,15)( 9,12)(10,14)(11,16);
s3 := Sym(16)!( 1,12)( 2,11)( 5, 8)( 6, 7)(13,14)(15,16);
poly := sub<Sym(16)|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, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2 >;

References