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Polytope of Type {3,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {3,2,6,8}
Number of vertices, edges, etc : 3, 3, 12, 48, 16
Order of s0s1s2s3s4 : 12
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 : {3,2,3,8}*576, {3,2,6,4}*576
   4-fold quotients : {3,2,3,4}*288, {3,2,6,4}*288b, {3,2,6,4}*288c
   8-fold quotients : {3,2,3,4}*144, {3,2,6,2}*144
   16-fold quotients : {3,2,3,2}*72
   24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)(18,27)
(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)(42,50)
(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)(66,75)
(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)(90,98)
(91,99);;
s3 := ( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)(13,53)
(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)(24,74)
(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)(35,88)
(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)(46,94)
(47,95)(48,99)(49,98)(50,97)(51,96);;
s4 := ( 4,34)( 5,35)( 6,32)( 7,33)( 8,31)( 9,30)(10,29)(11,28)(12,42)(13,43)
(14,40)(15,41)(16,39)(17,38)(18,37)(19,36)(20,50)(21,51)(22,48)(23,49)(24,47)
(25,46)(26,45)(27,44)(52,82)(53,83)(54,80)(55,81)(56,79)(57,78)(58,77)(59,76)
(60,90)(61,91)(62,88)(63,89)(64,87)(65,86)(66,85)(67,84)(68,98)(69,99)(70,96)
(71,97)(72,95)(73,94)(74,93)(75,92);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 6, 8)( 7, 9)(10,11)(12,20)(13,21)(14,24)(15,25)(16,22)(17,23)
(18,27)(19,26)(28,29)(30,33)(31,32)(36,45)(37,44)(38,49)(39,48)(40,47)(41,46)
(42,50)(43,51)(54,56)(55,57)(58,59)(60,68)(61,69)(62,72)(63,73)(64,70)(65,71)
(66,75)(67,74)(76,77)(78,81)(79,80)(84,93)(85,92)(86,97)(87,96)(88,95)(89,94)
(90,98)(91,99);
s3 := Sym(99)!( 4,60)( 5,61)( 6,63)( 7,62)( 8,66)( 9,67)(10,64)(11,65)(12,52)
(13,53)(14,55)(15,54)(16,58)(17,59)(18,56)(19,57)(20,68)(21,69)(22,71)(23,70)
(24,74)(25,75)(26,72)(27,73)(28,85)(29,84)(30,86)(31,87)(32,91)(33,90)(34,89)
(35,88)(36,77)(37,76)(38,78)(39,79)(40,83)(41,82)(42,81)(43,80)(44,93)(45,92)
(46,94)(47,95)(48,99)(49,98)(50,97)(51,96);
s4 := Sym(99)!( 4,34)( 5,35)( 6,32)( 7,33)( 8,31)( 9,30)(10,29)(11,28)(12,42)
(13,43)(14,40)(15,41)(16,39)(17,38)(18,37)(19,36)(20,50)(21,51)(22,48)(23,49)
(24,47)(25,46)(26,45)(27,44)(52,82)(53,83)(54,80)(55,81)(56,79)(57,78)(58,77)
(59,76)(60,90)(61,91)(62,88)(63,89)(64,87)(65,86)(66,85)(67,84)(68,98)(69,99)
(70,96)(71,97)(72,95)(73,94)(74,93)(75,92);
poly := sub<Sym(99)|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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >; 
 

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