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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1090143)
Rank : 5
Schlafli Type : {2,4,12,2}
Number of vertices, edges, etc : 2, 8, 48, 24, 2
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 : {2,4,12,2}*384b, {2,4,12,2}*384c, {2,4,6,2}*384
   4-fold quotients : {2,2,12,2}*192, {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
   8-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
   12-fold quotients : {2,2,4,2}*64
   16-fold quotients : {2,2,3,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,52)( 4,51)( 5,54)( 6,53)( 7,56)( 8,55)( 9,58)(10,57)(11,60)(12,59)
(13,62)(14,61)(15,64)(16,63)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)(23,72)
(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,82)(34,81)
(35,84)(36,83)(37,86)(38,85)(39,88)(40,87)(41,90)(42,89)(43,92)(44,91)(45,94)
(46,93)(47,96)(48,95)(49,98)(50,97);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)
(38,46)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)
(75,87)(76,89)(77,88)(78,90)(79,95)(80,97)(81,96)(82,98)(83,91)(84,93)(85,92)
(86,94);;
s3 := ( 3,31)( 4,32)( 5,34)( 6,33)( 7,27)( 8,28)( 9,30)(10,29)(11,35)(12,36)
(13,38)(14,37)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)
(24,48)(25,50)(26,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)
(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)
(70,89)(71,95)(72,96)(73,98)(74,97);;
s4 := ( 99,100);;
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, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
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(100)!(1,2);
s1 := Sym(100)!( 3,52)( 4,51)( 5,54)( 6,53)( 7,56)( 8,55)( 9,58)(10,57)(11,60)
(12,59)(13,62)(14,61)(15,64)(16,63)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)
(23,72)(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,82)
(34,81)(35,84)(36,83)(37,86)(38,85)(39,88)(40,87)(41,90)(42,89)(43,92)(44,91)
(45,94)(46,93)(47,96)(48,95)(49,98)(50,97);
s2 := Sym(100)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)
(37,44)(38,46)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)
(70,74)(75,87)(76,89)(77,88)(78,90)(79,95)(80,97)(81,96)(82,98)(83,91)(84,93)
(85,92)(86,94);
s3 := Sym(100)!( 3,31)( 4,32)( 5,34)( 6,33)( 7,27)( 8,28)( 9,30)(10,29)(11,35)
(12,36)(13,38)(14,37)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)
(23,47)(24,48)(25,50)(26,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)
(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)
(69,90)(70,89)(71,95)(72,96)(73,98)(74,97);
s4 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
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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