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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*384b
if this polytope has a name.
Group : SmallGroup(384,20062)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 8, 48, 16
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2} of size 768
   {2,6,12,3} of size 1920
Vertex Figure Of :
   {2,2,6,12} of size 768
   {3,2,6,12} of size 1152
   {5,2,6,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,12}*192, {2,6,6}*192
   4-fold quotients : {2,3,6}*96, {2,6,3}*96
   8-fold quotients : {2,3,3}*48
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,12}*768b, {2,6,12}*768, {2,12,12}*768d, {4,6,12}*768b
   3-fold covers : {2,6,12}*1152c, {6,6,12}*1152c, {2,6,12}*1152d
   5-fold covers : {2,30,12}*1920a, {10,6,12}*1920b, {2,6,60}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)(17,26)
(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)(41,49)
(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)(65,74)
(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)(89,97)
(90,98);;
s2 := ( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)(12,52)
(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)(23,73)
(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)(34,87)
(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)(45,93)
(46,94)(47,98)(48,97)(49,96)(50,95);;
s3 := ( 3,33)( 4,34)( 5,30)( 6,29)( 7,31)( 8,32)( 9,27)(10,28)(11,49)(12,50)
(13,46)(14,45)(15,47)(16,48)(17,43)(18,44)(19,41)(20,42)(21,38)(22,37)(23,39)
(24,40)(25,35)(26,36)(51,81)(52,82)(53,78)(54,77)(55,79)(56,80)(57,75)(58,76)
(59,97)(60,98)(61,94)(62,93)(63,95)(64,96)(65,91)(66,92)(67,89)(68,90)(69,86)
(70,85)(71,87)(72,88)(73,83)(74,84);;
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*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 5, 7)( 6, 8)( 9,10)(11,19)(12,20)(13,23)(14,24)(15,21)(16,22)
(17,26)(18,25)(27,28)(29,32)(30,31)(35,44)(36,43)(37,48)(38,47)(39,46)(40,45)
(41,49)(42,50)(53,55)(54,56)(57,58)(59,67)(60,68)(61,71)(62,72)(63,69)(64,70)
(65,74)(66,73)(75,76)(77,80)(78,79)(83,92)(84,91)(85,96)(86,95)(87,94)(88,93)
(89,97)(90,98);
s2 := Sym(98)!( 3,59)( 4,60)( 5,62)( 6,61)( 7,65)( 8,66)( 9,63)(10,64)(11,51)
(12,52)(13,54)(14,53)(15,57)(16,58)(17,55)(18,56)(19,67)(20,68)(21,70)(22,69)
(23,73)(24,74)(25,71)(26,72)(27,84)(28,83)(29,85)(30,86)(31,90)(32,89)(33,88)
(34,87)(35,76)(36,75)(37,77)(38,78)(39,82)(40,81)(41,80)(42,79)(43,92)(44,91)
(45,93)(46,94)(47,98)(48,97)(49,96)(50,95);
s3 := Sym(98)!( 3,33)( 4,34)( 5,30)( 6,29)( 7,31)( 8,32)( 9,27)(10,28)(11,49)
(12,50)(13,46)(14,45)(15,47)(16,48)(17,43)(18,44)(19,41)(20,42)(21,38)(22,37)
(23,39)(24,40)(25,35)(26,36)(51,81)(52,82)(53,78)(54,77)(55,79)(56,80)(57,75)
(58,76)(59,97)(60,98)(61,94)(62,93)(63,95)(64,96)(65,91)(66,92)(67,89)(68,90)
(69,86)(70,85)(71,87)(72,88)(73,83)(74,84);
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*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 >; 
 

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