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Polytope of Type {2,4,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,4}*768e
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 5
Schlafli Type : {2,4,12,4}
Number of vertices, edges, etc : 2, 4, 24, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,12,2}*384c, {2,4,6,4}*384c
   4-fold quotients : {2,4,6,2}*192c
   8-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,29)( 4,30)( 5,27)( 6,28)( 7,33)( 8,34)( 9,31)(10,32)(11,37)(12,38)
(13,35)(14,36)(15,41)(16,42)(17,39)(18,40)(19,45)(20,46)(21,43)(22,44)(23,49)
(24,50)(25,47)(26,48)(51,77)(52,78)(53,75)(54,76)(55,81)(56,82)(57,79)(58,80)
(59,85)(60,86)(61,83)(62,84)(63,89)(64,90)(65,87)(66,88)(67,93)(68,94)(69,91)
(70,92)(71,97)(72,98)(73,95)(74,96);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(51,75)
(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)(62,82)
(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)(73,92)
(74,94);;
s3 := ( 3,59)( 4,62)( 5,61)( 6,60)( 7,55)( 8,58)( 9,57)(10,56)(11,51)(12,54)
(13,53)(14,52)(15,71)(16,74)(17,73)(18,72)(19,67)(20,70)(21,69)(22,68)(23,63)
(24,66)(25,65)(26,64)(27,83)(28,86)(29,85)(30,84)(31,79)(32,82)(33,81)(34,80)
(35,75)(36,78)(37,77)(38,76)(39,95)(40,98)(41,97)(42,96)(43,91)(44,94)(45,93)
(46,92)(47,87)(48,90)(49,89)(50,88);;
s4 := (51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)
(61,73)(62,74)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)
(84,96)(85,97)(86,98);;
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*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3,29)( 4,30)( 5,27)( 6,28)( 7,33)( 8,34)( 9,31)(10,32)(11,37)
(12,38)(13,35)(14,36)(15,41)(16,42)(17,39)(18,40)(19,45)(20,46)(21,43)(22,44)
(23,49)(24,50)(25,47)(26,48)(51,77)(52,78)(53,75)(54,76)(55,81)(56,82)(57,79)
(58,80)(59,85)(60,86)(61,83)(62,84)(63,89)(64,90)(65,87)(66,88)(67,93)(68,94)
(69,91)(70,92)(71,97)(72,98)(73,95)(74,96);
s2 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)
(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)
(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)
(73,92)(74,94);
s3 := Sym(98)!( 3,59)( 4,62)( 5,61)( 6,60)( 7,55)( 8,58)( 9,57)(10,56)(11,51)
(12,54)(13,53)(14,52)(15,71)(16,74)(17,73)(18,72)(19,67)(20,70)(21,69)(22,68)
(23,63)(24,66)(25,65)(26,64)(27,83)(28,86)(29,85)(30,84)(31,79)(32,82)(33,81)
(34,80)(35,75)(36,78)(37,77)(38,76)(39,95)(40,98)(41,97)(42,96)(43,91)(44,94)
(45,93)(46,92)(47,87)(48,90)(49,89)(50,88);
s4 := Sym(98)!(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)
(60,72)(61,73)(62,74)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)
(83,95)(84,96)(85,97)(86,98);
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*s1*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 >; 
 

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