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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,4}*768b
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 5
Schlafli Type : {2,3,4,4}
Number of vertices, edges, etc : 2, 6, 24, 32, 8
Order of s0s1s2s3s4 : 6
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 : {2,3,4,4}*384a
   4-fold quotients : {2,3,4,2}*192
   8-fold quotients : {2,3,4,2}*96
   16-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)(22,37)
(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)(33,50)
(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)(70,85)
(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)(81,98)
(82,97);;
s2 := ( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)(12,34)
(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(36,38)(40,42)(43,47)(44,50)(45,49)
(46,48)(51,67)(52,70)(53,69)(54,68)(55,71)(56,74)(57,73)(58,72)(59,79)(60,82)
(61,81)(62,80)(63,75)(64,78)(65,77)(66,76)(84,86)(88,90)(91,95)(92,98)(93,97)
(94,96);;
s3 := ( 3,63)( 4,64)( 5,65)( 6,66)( 7,59)( 8,60)( 9,61)(10,62)(11,55)(12,56)
(13,57)(14,58)(15,51)(16,52)(17,53)(18,54)(19,79)(20,80)(21,81)(22,82)(23,75)
(24,76)(25,77)(26,78)(27,71)(28,72)(29,73)(30,74)(31,67)(32,68)(33,69)(34,70)
(35,95)(36,96)(37,97)(38,98)(39,91)(40,92)(41,93)(42,94)(43,87)(44,88)(45,89)
(46,90)(47,83)(48,84)(49,85)(50,86);;
s4 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)
(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)
(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)
(91,94)(92,93)(95,96)(97,98);;
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, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s1*s2*s3*s4*s3*s2*s3*s1*s2*s3*s4*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13)(17,18)(19,35)(20,36)(21,38)
(22,37)(23,43)(24,44)(25,46)(26,45)(27,39)(28,40)(29,42)(30,41)(31,47)(32,48)
(33,50)(34,49)(53,54)(55,59)(56,60)(57,62)(58,61)(65,66)(67,83)(68,84)(69,86)
(70,85)(71,91)(72,92)(73,94)(74,93)(75,87)(76,88)(77,90)(78,89)(79,95)(80,96)
(81,98)(82,97);
s2 := Sym(98)!( 3,19)( 4,22)( 5,21)( 6,20)( 7,23)( 8,26)( 9,25)(10,24)(11,31)
(12,34)(13,33)(14,32)(15,27)(16,30)(17,29)(18,28)(36,38)(40,42)(43,47)(44,50)
(45,49)(46,48)(51,67)(52,70)(53,69)(54,68)(55,71)(56,74)(57,73)(58,72)(59,79)
(60,82)(61,81)(62,80)(63,75)(64,78)(65,77)(66,76)(84,86)(88,90)(91,95)(92,98)
(93,97)(94,96);
s3 := Sym(98)!( 3,63)( 4,64)( 5,65)( 6,66)( 7,59)( 8,60)( 9,61)(10,62)(11,55)
(12,56)(13,57)(14,58)(15,51)(16,52)(17,53)(18,54)(19,79)(20,80)(21,81)(22,82)
(23,75)(24,76)(25,77)(26,78)(27,71)(28,72)(29,73)(30,74)(31,67)(32,68)(33,69)
(34,70)(35,95)(36,96)(37,97)(38,98)(39,91)(40,92)(41,93)(42,94)(43,87)(44,88)
(45,89)(46,90)(47,83)(48,84)(49,85)(50,86);
s4 := Sym(98)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)
(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)
(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)
(88,90)(91,94)(92,93)(95,96)(97,98);
poly := sub<Sym(98)|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, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s1*s2*s3*s4*s3*s2*s3*s1*s2*s3*s4*s3*s2 >; 
 

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