Polytope of Type {6,2,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,40}*960
if this polytope has a name.
Group : SmallGroup(960,8160)
Rank : 4
Schlafli Type : {6,2,40}
Number of vertices, edges, etc : 6, 6, 40, 40
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,40,2} of size 1920
Vertex Figure Of :
   {2,6,2,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,40}*480, {6,2,20}*480
   3-fold quotients : {2,2,40}*320
   4-fold quotients : {3,2,20}*240, {6,2,10}*240
   5-fold quotients : {6,2,8}*192
   6-fold quotients : {2,2,20}*160
   8-fold quotients : {3,2,10}*120, {6,2,5}*120
   10-fold quotients : {3,2,8}*96, {6,2,4}*96
   12-fold quotients : {2,2,10}*80
   15-fold quotients : {2,2,8}*64
   16-fold quotients : {3,2,5}*60
   20-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {2,2,5}*40
   30-fold quotients : {2,2,4}*32
   40-fold quotients : {3,2,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,4,40}*1920a, {12,2,40}*1920, {6,2,80}*1920
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,27)(22,26)(23,29)
(24,28)(31,36)(32,35)(33,38)(34,37)(39,40)(41,44)(42,43)(45,46);;
s3 := ( 7,13)( 8,10)( 9,21)(11,23)(12,16)(14,18)(15,31)(17,33)(19,24)(20,26)
(22,28)(25,39)(27,41)(29,34)(30,35)(32,37)(36,45)(38,42)(40,43)(44,46);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(46)!(3,4)(5,6);
s1 := Sym(46)!(1,5)(2,3)(4,6);
s2 := Sym(46)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,27)(22,26)
(23,29)(24,28)(31,36)(32,35)(33,38)(34,37)(39,40)(41,44)(42,43)(45,46);
s3 := Sym(46)!( 7,13)( 8,10)( 9,21)(11,23)(12,16)(14,18)(15,31)(17,33)(19,24)
(20,26)(22,28)(25,39)(27,41)(29,34)(30,35)(32,37)(36,45)(38,42)(40,43)(44,46);
poly := sub<Sym(46)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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