Polytope of Type {8,6,6} with group SmallGroup(1920,240560)

Overview

Group: SmallGroup(1920,240560)
Rank: 4
Schläfli Type: {8,6,6}
Vertices, edges, …: 8, 80, 60, 20
Order of s₀s₁s₂s₃: 24
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

{4,6,6}*960

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 := ( 6,18)( 7,19)( 8,21)( 9,20)(10,14)(11,15)(12,17)(13,16)(22,34)(23,35)(24,37)(25,36)(26,30)(27,31)(28,33)(29,32);;
s1 := ( 2, 3)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);;
s2 := ( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);;
s3 := (2,4)(3,5);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(37)!( 6,18)( 7,19)( 8,21)( 9,20)(10,14)(11,15)(12,17)(13,16)(22,34)(23,35)(24,37)(25,36)(26,30)(27,31)(28,33)(29,32);
s1 := Sym(37)!( 2, 3)( 4, 5)( 6,26)( 7,27)( 8,29)( 9,28)(10,22)(11,23)(12,25)(13,24)(14,36)(15,37)(16,34)(17,35)(18,32)(19,33)(20,30)(21,31);
s2 := Sym(37)!( 1, 2)( 6,10)( 7,11)( 8,12)( 9,13)(14,18)(15,19)(16,20)(17,21)(22,26)(23,27)(24,28)(25,29)(30,34)(31,35)(32,36)(33,37);
s3 := Sym(37)!(2,4)(3,5);
poly := sub<Sym(37)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References