Polytope of Type {2,6,20}

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

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