Polytope of Type {6,2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,4,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,205034)
Rank : 5
Schlafli Type : {6,2,4,20}
Number of vertices, edges, etc : 6, 6, 4, 40, 20
Order of s₀s₁s₂s₃s₄ : 60
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 : {3,2,4,20}*960, {6,2,2,20}*960, {6,2,4,10}*960
   3-fold quotients : {2,2,4,20}*640
   4-fold quotients : {3,2,2,20}*480, {3,2,4,10}*480, {6,2,2,10}*480
   5-fold quotients : {6,2,4,4}*384
   6-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320
   8-fold quotients : {3,2,2,10}*240, {6,2,2,5}*240
   10-fold quotients : {3,2,4,4}*192, {6,2,2,4}*192, {6,2,4,2}*192
   12-fold quotients : {2,2,2,10}*160
   15-fold quotients : {2,2,4,4}*128
   16-fold quotients : {3,2,2,5}*120
   20-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {6,2,2,2}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,2,4}*64, {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 := ( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)
(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,72)
(28,73)(29,74)(30,75)(31,76)(32,67)(33,68)(34,69)(35,70)(36,71)(37,82)(38,83)
(39,84)(40,85)(41,86)(42,77)(43,78)(44,79)(45,80)(46,81);;
s3 := ( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)(16,33)
(17,37)(18,41)(19,40)(20,39)(21,38)(22,42)(23,46)(24,45)(25,44)(26,43)(47,67)
(48,71)(49,70)(50,69)(51,68)(52,72)(53,76)(54,75)(55,74)(56,73)(57,77)(58,81)
(59,80)(60,79)(61,78)(62,82)(63,86)(64,85)(65,84)(66,83);;
s4 := ( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,38)(28,37)
(29,41)(30,40)(31,39)(32,43)(33,42)(34,46)(35,45)(36,44)(47,48)(49,51)(52,53)
(54,56)(57,58)(59,61)(62,63)(64,66)(67,78)(68,77)(69,81)(70,80)(71,79)(72,83)
(73,82)(74,86)(75,85)(76,84);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(86)!(3,4)(5,6);
s1 := Sym(86)!(1,5)(2,3)(4,6);
s2 := Sym(86)!( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)
(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)
(27,72)(28,73)(29,74)(30,75)(31,76)(32,67)(33,68)(34,69)(35,70)(36,71)(37,82)
(38,83)(39,84)(40,85)(41,86)(42,77)(43,78)(44,79)(45,80)(46,81);
s3 := Sym(86)!( 7,27)( 8,31)( 9,30)(10,29)(11,28)(12,32)(13,36)(14,35)(15,34)
(16,33)(17,37)(18,41)(19,40)(20,39)(21,38)(22,42)(23,46)(24,45)(25,44)(26,43)
(47,67)(48,71)(49,70)(50,69)(51,68)(52,72)(53,76)(54,75)(55,74)(56,73)(57,77)
(58,81)(59,80)(60,79)(61,78)(62,82)(63,86)(64,85)(65,84)(66,83);
s4 := Sym(86)!( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,38)
(28,37)(29,41)(30,40)(31,39)(32,43)(33,42)(34,46)(35,45)(36,44)(47,48)(49,51)
(52,53)(54,56)(57,58)(59,61)(62,63)(64,66)(67,78)(68,77)(69,81)(70,80)(71,79)
(72,83)(73,82)(74,86)(75,85)(76,84);
poly := sub<Sym(86)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope