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Polytope of Type {3,2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98791)
Rank : 5
Schlafli Type : {3,2,4,24}
Number of vertices, edges, etc : 3, 3, 4, 48, 24
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 : {3,2,4,12}*576a
   3-fold quotients : {3,2,4,8}*384b
   4-fold quotients : {3,2,2,12}*288, {3,2,4,6}*288a
   6-fold quotients : {3,2,4,4}*192
   8-fold quotients : {3,2,2,6}*144
   12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   16-fold quotients : {3,2,2,3}*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 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)
(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(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)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)(46,91)
(47,92)(48,93)(49,88)(50,89)(51,90);;
s3 := ( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)(13,37)
(14,39)(15,38)(16,43)(17,45)(18,44)(19,40)(20,42)(21,41)(22,49)(23,51)(24,50)
(25,46)(26,48)(27,47)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)(59,84)
(60,83)(61,85)(62,87)(63,86)(64,91)(65,93)(66,92)(67,88)(68,90)(69,89)(70,97)
(71,99)(72,98)(73,94)(74,96)(75,95);;
s4 := ( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,23)(25,26)
(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,50)(35,49)(36,51)(37,47)(38,46)
(39,48)(52,53)(55,56)(58,62)(59,61)(60,63)(64,68)(65,67)(66,69)(70,71)(73,74)
(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,98)(83,97)(84,99)(85,95)(86,94)
(87,96);;
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, 
s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(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)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)
(46,91)(47,92)(48,93)(49,88)(50,89)(51,90);
s3 := Sym(99)!( 4,28)( 5,30)( 6,29)( 7,31)( 8,33)( 9,32)(10,34)(11,36)(12,35)
(13,37)(14,39)(15,38)(16,43)(17,45)(18,44)(19,40)(20,42)(21,41)(22,49)(23,51)
(24,50)(25,46)(26,48)(27,47)(52,76)(53,78)(54,77)(55,79)(56,81)(57,80)(58,82)
(59,84)(60,83)(61,85)(62,87)(63,86)(64,91)(65,93)(66,92)(67,88)(68,90)(69,89)
(70,97)(71,99)(72,98)(73,94)(74,96)(75,95);
s4 := Sym(99)!( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,20)(17,19)(18,21)(22,23)
(25,26)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,50)(35,49)(36,51)(37,47)
(38,46)(39,48)(52,53)(55,56)(58,62)(59,61)(60,63)(64,68)(65,67)(66,69)(70,71)
(73,74)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,98)(83,97)(84,99)(85,95)
(86,94)(87,96);
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, s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3 >; 
 

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