Polytope of Type {6,2,40,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,40,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235349)
Rank : 5
Schlafli Type : {6,2,40,2}
Number of vertices, edges, etc : 6, 6, 40, 40, 2
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,40,2}*960, {6,2,20,2}*960
   3-fold quotients : {2,2,40,2}*640
   4-fold quotients : {3,2,20,2}*480, {6,2,10,2}*480
   5-fold quotients : {6,2,8,2}*384
   6-fold quotients : {2,2,20,2}*320
   8-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
   10-fold quotients : {3,2,8,2}*192, {6,2,4,2}*192
   12-fold quotients : {2,2,10,2}*160
   15-fold quotients : {2,2,8,2}*128
   16-fold quotients : {3,2,5,2}*120
   20-fold quotients : {3,2,4,2}*96, {6,2,2,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,4,2}*64
   40-fold quotients : {3,2,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s4 := (47,48);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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(48)!(3,4)(5,6);
s1 := Sym(48)!(1,5)(2,3)(4,6);
s2 := Sym(48)!( 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(48)!( 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);
s4 := Sym(48)!(47,48);
poly := sub<Sym(48)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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