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Polytope of Type {3,2,12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,97531)
Rank : 5
Schlafli Type : {3,2,12,8}
Number of vertices, edges, etc : 3, 3, 12, 48, 8
Order of s0s1s2s3s4 : 24
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 : {3,2,12,4}*576a, {3,2,6,8}*576
   3-fold quotients : {3,2,4,8}*384a
   4-fold quotients : {3,2,12,2}*288, {3,2,6,4}*288a
   6-fold quotients : {3,2,4,4}*192, {3,2,2,8}*192
   8-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   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 := ( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,40)(29,42)
(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47)(37,49)(38,51)(39,50)(53,54)
(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75)(76,88)(77,90)(78,89)(79,91)
(80,93)(81,92)(82,94)(83,96)(84,95)(85,97)(86,99)(87,98);;
s3 := ( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,38)(11,37)(12,39)(13,35)
(14,34)(15,36)(16,41)(17,40)(18,42)(19,44)(20,43)(21,45)(22,50)(23,49)(24,51)
(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,86)(59,85)
(60,87)(61,83)(62,82)(63,84)(64,89)(65,88)(66,90)(67,92)(68,91)(69,93)(70,98)
(71,97)(72,99)(73,95)(74,94)(75,96);;
s4 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,61)(11,62)(12,63)(13,58)
(14,59)(15,60)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,73)(23,74)(24,75)
(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)(35,77)
(36,78)(37,79)(38,80)(39,81)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,88)
(47,89)(48,90)(49,91)(50,92)(51,93);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,40)
(29,42)(30,41)(31,43)(32,45)(33,44)(34,46)(35,48)(36,47)(37,49)(38,51)(39,50)
(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72)(74,75)(76,88)(77,90)(78,89)
(79,91)(80,93)(81,92)(82,94)(83,96)(84,95)(85,97)(86,99)(87,98);
s3 := Sym(99)!( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,38)(11,37)(12,39)
(13,35)(14,34)(15,36)(16,41)(17,40)(18,42)(19,44)(20,43)(21,45)(22,50)(23,49)
(24,51)(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,86)
(59,85)(60,87)(61,83)(62,82)(63,84)(64,89)(65,88)(66,90)(67,92)(68,91)(69,93)
(70,98)(71,97)(72,99)(73,95)(74,94)(75,96);
s4 := Sym(99)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,61)(11,62)(12,63)
(13,58)(14,59)(15,60)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,73)(23,74)
(24,75)(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,81)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)
(46,88)(47,89)(48,90)(49,91)(50,92)(51,93);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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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