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Polytope of Type {6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 16, 96, 32, 2
Order of s0s1s2s3 : 8
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 : {6,12,2}*384a, {6,12,2}*384b, {6,6,2}*384b
   4-fold quotients : {3,12,2}*192, {6,6,2}*192
   8-fold quotients : {3,6,2}*96, {6,3,2}*96
   16-fold quotients : {3,3,2}*48
   24-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)(15,24)
(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)(39,48)
(40,47)(49,50)(51,53)(52,54)(57,66)(58,65)(59,69)(60,70)(61,67)(62,68)(63,71)
(64,72)(73,74)(75,77)(76,78)(81,90)(82,89)(83,93)(84,94)(85,91)(86,92)(87,95)
(88,96);;
s1 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)
(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)(45,47)
(46,48)(49,82)(50,81)(51,83)(52,84)(53,88)(54,87)(55,86)(56,85)(57,74)(58,73)
(59,75)(60,76)(61,80)(62,79)(63,78)(64,77)(65,90)(66,89)(67,91)(68,92)(69,96)
(70,95)(71,94)(72,93);;
s2 := ( 1,55)( 2,56)( 3,51)( 4,52)( 5,54)( 6,53)( 7,49)( 8,50)( 9,71)(10,72)
(11,67)(12,68)(13,70)(14,69)(15,65)(16,66)(17,63)(18,64)(19,59)(20,60)(21,62)
(22,61)(23,57)(24,58)(25,79)(26,80)(27,75)(28,76)(29,78)(30,77)(31,73)(32,74)
(33,95)(34,96)(35,91)(36,92)(37,94)(38,93)(39,89)(40,90)(41,87)(42,88)(43,83)
(44,84)(45,86)(46,85)(47,81)(48,82);;
s3 := (97,98);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)
(15,24)(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)
(39,48)(40,47)(49,50)(51,53)(52,54)(57,66)(58,65)(59,69)(60,70)(61,67)(62,68)
(63,71)(64,72)(73,74)(75,77)(76,78)(81,90)(82,89)(83,93)(84,94)(85,91)(86,92)
(87,95)(88,96);
s1 := Sym(98)!( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)
(21,23)(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)
(45,47)(46,48)(49,82)(50,81)(51,83)(52,84)(53,88)(54,87)(55,86)(56,85)(57,74)
(58,73)(59,75)(60,76)(61,80)(62,79)(63,78)(64,77)(65,90)(66,89)(67,91)(68,92)
(69,96)(70,95)(71,94)(72,93);
s2 := Sym(98)!( 1,55)( 2,56)( 3,51)( 4,52)( 5,54)( 6,53)( 7,49)( 8,50)( 9,71)
(10,72)(11,67)(12,68)(13,70)(14,69)(15,65)(16,66)(17,63)(18,64)(19,59)(20,60)
(21,62)(22,61)(23,57)(24,58)(25,79)(26,80)(27,75)(28,76)(29,78)(30,77)(31,73)
(32,74)(33,95)(34,96)(35,91)(36,92)(37,94)(38,93)(39,89)(40,90)(41,87)(42,88)
(43,83)(44,84)(45,86)(46,85)(47,81)(48,82);
s3 := Sym(98)!(97,98);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >; 
 

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