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Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*768d
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 16, 96, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 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}*384b, {2,4,6}*384b, {2,4,12}*384c
   4-fold quotients : {2,4,12}*192a, {2,4,12}*192b, {2,4,12}*192c, {2,4,6}*192
   8-fold quotients : {2,2,12}*96, {2,4,6}*96a, {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   12-fold quotients : {2,4,4}*64
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)
(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)
(44,46)(47,49)(48,50)(51,65)(52,66)(53,63)(54,64)(55,69)(56,70)(57,67)(58,68)
(59,73)(60,74)(61,71)(62,72)(75,89)(76,90)(77,87)(78,88)(79,93)(80,94)(81,91)
(82,92)(83,97)(84,98)(85,95)(86,96);;
s2 := ( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)(12,57)
(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)(23,67)
(24,69)(25,68)(26,70)(27,75)(28,77)(29,76)(30,78)(31,83)(32,85)(33,84)(34,86)
(35,79)(36,81)(37,80)(38,82)(39,87)(40,89)(41,88)(42,90)(43,95)(44,97)(45,96)
(46,98)(47,91)(48,93)(49,92)(50,94);;
s3 := ( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)(20,22)
(27,35)(28,38)(29,37)(30,36)(32,34)(39,47)(40,50)(41,49)(42,48)(44,46)(51,83)
(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)(60,78)(61,77)(62,76)
(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)(71,87)(72,90)(73,89)
(74,88);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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(98)!(1,2);
s1 := Sym(98)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)
(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)
(43,45)(44,46)(47,49)(48,50)(51,65)(52,66)(53,63)(54,64)(55,69)(56,70)(57,67)
(58,68)(59,73)(60,74)(61,71)(62,72)(75,89)(76,90)(77,87)(78,88)(79,93)(80,94)
(81,91)(82,92)(83,97)(84,98)(85,95)(86,96);
s2 := Sym(98)!( 3,51)( 4,53)( 5,52)( 6,54)( 7,59)( 8,61)( 9,60)(10,62)(11,55)
(12,57)(13,56)(14,58)(15,63)(16,65)(17,64)(18,66)(19,71)(20,73)(21,72)(22,74)
(23,67)(24,69)(25,68)(26,70)(27,75)(28,77)(29,76)(30,78)(31,83)(32,85)(33,84)
(34,86)(35,79)(36,81)(37,80)(38,82)(39,87)(40,89)(41,88)(42,90)(43,95)(44,97)
(45,96)(46,98)(47,91)(48,93)(49,92)(50,94);
s3 := Sym(98)!( 3,11)( 4,14)( 5,13)( 6,12)( 8,10)(15,23)(16,26)(17,25)(18,24)
(20,22)(27,35)(28,38)(29,37)(30,36)(32,34)(39,47)(40,50)(41,49)(42,48)(44,46)
(51,83)(52,86)(53,85)(54,84)(55,79)(56,82)(57,81)(58,80)(59,75)(60,78)(61,77)
(62,76)(63,95)(64,98)(65,97)(66,96)(67,91)(68,94)(69,93)(70,92)(71,87)(72,90)
(73,89)(74,88);
poly := sub<Sym(98)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*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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