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Polytope of Type {2,30,6}

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

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