Polytope of Type {20,6,2}

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

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

Permutation Representation (Magma) :

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

to this polytope