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Polytope of Type {84,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {84,2,4}*1344
if this polytope has a name.
Group : SmallGroup(1344,10931)
Rank : 4
Schlafli Type : {84,2,4}
Number of vertices, edges, etc : 84, 84, 4, 4
Order of s0s1s2s3 : 84
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 : {84,2,2}*672, {42,2,4}*672
   3-fold quotients : {28,2,4}*448
   4-fold quotients : {21,2,4}*336, {42,2,2}*336
   6-fold quotients : {28,2,2}*224, {14,2,4}*224
   7-fold quotients : {12,2,4}*192
   8-fold quotients : {21,2,2}*168
   12-fold quotients : {7,2,4}*112, {14,2,2}*112
   14-fold quotients : {12,2,2}*96, {6,2,4}*96
   21-fold quotients : {4,2,4}*64
   24-fold quotients : {7,2,2}*56
   28-fold quotients : {3,2,4}*48, {6,2,2}*48
   42-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {3,2,2}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)(14,16)
(23,28)(24,27)(25,26)(29,36)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,64)
(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,78)(51,84)(52,83)(53,82)(54,81)
(55,80)(56,79)(57,71)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72);;
s1 := ( 1,51)( 2,50)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,44)( 9,43)(10,49)
(11,48)(12,47)(13,46)(14,45)(15,58)(16,57)(17,63)(18,62)(19,61)(20,60)(21,59)
(22,72)(23,71)(24,77)(25,76)(26,75)(27,74)(28,73)(29,65)(30,64)(31,70)(32,69)
(33,68)(34,67)(35,66)(36,79)(37,78)(38,84)(39,83)(40,82)(41,81)(42,80);;
s2 := (86,87);;
s3 := (85,86)(87,88);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(88)!( 2, 7)( 3, 6)( 4, 5)( 8,15)( 9,21)(10,20)(11,19)(12,18)(13,17)
(14,16)(23,28)(24,27)(25,26)(29,36)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)
(43,64)(44,70)(45,69)(46,68)(47,67)(48,66)(49,65)(50,78)(51,84)(52,83)(53,82)
(54,81)(55,80)(56,79)(57,71)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72);
s1 := Sym(88)!( 1,51)( 2,50)( 3,56)( 4,55)( 5,54)( 6,53)( 7,52)( 8,44)( 9,43)
(10,49)(11,48)(12,47)(13,46)(14,45)(15,58)(16,57)(17,63)(18,62)(19,61)(20,60)
(21,59)(22,72)(23,71)(24,77)(25,76)(26,75)(27,74)(28,73)(29,65)(30,64)(31,70)
(32,69)(33,68)(34,67)(35,66)(36,79)(37,78)(38,84)(39,83)(40,82)(41,81)(42,80);
s2 := Sym(88)!(86,87);
s3 := Sym(88)!(85,86)(87,88);
poly := sub<Sym(88)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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