Polytope of Type {2,20,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5921)
Rank : 4
Schlafli Type : {2,20,6}
Number of vertices, edges, etc : 2, 60, 180, 18
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,20,6}*720
   5-fold quotients : {2,4,6}*288
   9-fold quotients : {2,20,2}*160
   10-fold quotients : {2,4,6}*144
   18-fold quotients : {2,10,2}*80
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {2,4,2}*32
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,18)( 9,22)(10,21)(11,20)(12,19)(13,33)(14,37)(15,36)
(16,35)(17,34)(24,27)(25,26)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)(45,46)
(49,52)(50,51)(53,63)(54,67)(55,66)(56,65)(57,64)(58,78)(59,82)(60,81)(61,80)
(62,79)(69,72)(70,71)(73,83)(74,87)(75,86)(76,85)(77,84)(89,92)(90,91);;
s2 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)
(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)(42,45)
(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)(69,73)
(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90);;
s3 := ( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)(12,67)
(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)(23,48)
(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)(34,84)
(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)(45,90)
(46,91)(47,92);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(92)!(1,2);
s1 := Sym(92)!( 4, 7)( 5, 6)( 8,18)( 9,22)(10,21)(11,20)(12,19)(13,33)(14,37)
(15,36)(16,35)(17,34)(24,27)(25,26)(28,38)(29,42)(30,41)(31,40)(32,39)(44,47)
(45,46)(49,52)(50,51)(53,63)(54,67)(55,66)(56,65)(57,64)(58,78)(59,82)(60,81)
(61,80)(62,79)(69,72)(70,71)(73,83)(74,87)(75,86)(76,85)(77,84)(89,92)(90,91);
s2 := Sym(92)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)
(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)
(42,45)(48,49)(50,52)(53,59)(54,58)(55,62)(56,61)(57,60)(63,64)(65,67)(68,74)
(69,73)(70,77)(71,76)(72,75)(78,79)(80,82)(83,89)(84,88)(85,92)(86,91)(87,90);
s3 := Sym(92)!( 3,68)( 4,69)( 5,70)( 6,71)( 7,72)( 8,63)( 9,64)(10,65)(11,66)
(12,67)(13,73)(14,74)(15,75)(16,76)(17,77)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,48)(24,49)(25,50)(26,51)(27,52)(28,58)(29,59)(30,60)(31,61)(32,62)(33,83)
(34,84)(35,85)(36,86)(37,87)(38,78)(39,79)(40,80)(41,81)(42,82)(43,88)(44,89)
(45,90)(46,91)(47,92);
poly := sub<Sym(92)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope