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Polytope of Type {2,6,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,10}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {2,6,6,10}
Number of vertices, edges, etc : 2, 6, 18, 30, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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 : {2,3,6,10}*720
   3-fold quotients : {2,6,2,10}*480
   5-fold quotients : {2,6,6,2}*288c
   6-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   9-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,3,6,2}*144
   12-fold quotients : {2,3,2,5}*120
   15-fold quotients : {2,6,2,2}*96
   18-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,3,2,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)(22,37)
(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42)(53,58)
(54,59)(55,60)(56,61)(57,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,88)(69,89)
(70,90)(71,91)(72,92)(73,83)(74,84)(75,85)(76,86)(77,87);;
s2 := ( 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);;
s3 := ( 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);;
s4 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)
(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)(80,82)
(83,84)(85,87)(88,89)(90,92);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(92)!(1,2);
s1 := Sym(92)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)
(22,37)(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42)
(53,58)(54,59)(55,60)(56,61)(57,62)(63,78)(64,79)(65,80)(66,81)(67,82)(68,88)
(69,89)(70,90)(71,91)(72,92)(73,83)(74,84)(75,85)(76,86)(77,87);
s2 := 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);
s3 := 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);
s4 := Sym(92)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)
(53,54)(55,57)(58,59)(60,62)(63,64)(65,67)(68,69)(70,72)(73,74)(75,77)(78,79)
(80,82)(83,84)(85,87)(88,89)(90,92);
poly := sub<Sym(92)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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