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

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

to this polytope