Polytope of Type {8,6,10} with group SmallGroup(1920,240561)

Overview

Group: SmallGroup(1920,240561)
Rank: 4
Schläfli Type: {8,6,10}
Vertices, edges, …: 8, 48, 60, 20
Order of s₀s₁s₂s₃: 40
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

8-fold

16-fold

{2,3,5}*120

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12);;
s1 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,21)(19,20);;
s2 := (17,20)(18,21);;
s3 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,19)(20,21);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(21)!( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12);
s1 := Sym(21)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(18,21)(19,20);
s2 := Sym(21)!(17,20)(18,21);
s3 := Sym(21)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,19)(20,21);
poly := sub<Sym(21)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3 >;

References