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Polytope of Type {2,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,30}*720b
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 4
Schlafli Type : {2,6,30}
Number of vertices, edges, etc : 2, 6, 90, 30
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,30,2} of size 1440
Vertex Figure Of :
   {2,2,6,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,10}*240, {2,2,30}*240
   5-fold quotients : {2,6,6}*144a
   6-fold quotients : {2,2,15}*120
   9-fold quotients : {2,2,10}*80
   15-fold quotients : {2,2,6}*48, {2,6,2}*48
   18-fold quotients : {2,2,5}*40
   30-fold quotients : {2,2,3}*24, {2,3,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,30}*1440b, {2,6,60}*1440b, {4,6,30}*1440b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)
(28,43)(29,44)(30,45)(31,46)(32,47)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)
(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92);;
s2 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)
(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)
(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)
(87,89);;
s3 := ( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)(12,50)
(13,59)(14,58)(15,62)(16,61)(17,60)(18,69)(19,68)(20,72)(21,71)(22,70)(23,64)
(24,63)(25,67)(26,66)(27,65)(28,74)(29,73)(30,77)(31,76)(32,75)(33,84)(34,83)
(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)(45,92)
(46,91)(47,90);;
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*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*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*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)!(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)
(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(63,78)(64,79)(65,80)(66,81)(67,82)
(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92);
s2 := Sym(92)!( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)
(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)
(41,45)(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)
(57,74)(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)
(86,90)(87,89);
s3 := Sym(92)!( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)
(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,69)(19,68)(20,72)(21,71)(22,70)
(23,64)(24,63)(25,67)(26,66)(27,65)(28,74)(29,73)(30,77)(31,76)(32,75)(33,84)
(34,83)(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)
(45,92)(46,91)(47,90);
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*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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