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Polytope of Type {6,2,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,56}*1344
if this polytope has a name.
Group : SmallGroup(1344,8483)
Rank : 4
Schlafli Type : {6,2,56}
Number of vertices, edges, etc : 6, 6, 56, 56
Order of s0s1s2s3 : 168
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 : {3,2,56}*672, {6,2,28}*672
   3-fold quotients : {2,2,56}*448
   4-fold quotients : {3,2,28}*336, {6,2,14}*336
   6-fold quotients : {2,2,28}*224
   7-fold quotients : {6,2,8}*192
   8-fold quotients : {3,2,14}*168, {6,2,7}*168
   12-fold quotients : {2,2,14}*112
   14-fold quotients : {3,2,8}*96, {6,2,4}*96
   16-fold quotients : {3,2,7}*84
   21-fold quotients : {2,2,8}*64
   24-fold quotients : {2,2,7}*56
   28-fold quotients : {3,2,4}*48, {6,2,2}*48
   42-fold quotients : {2,2,4}*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 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,27)(22,26)(23,29)
(24,28)(30,31)(33,40)(34,39)(35,42)(36,41)(37,44)(38,43)(45,46)(47,52)(48,51)
(49,54)(50,53)(55,56)(57,60)(58,59)(61,62);;
s3 := ( 7,13)( 8,10)( 9,21)(11,23)(12,16)(14,18)(15,33)(17,35)(19,37)(20,26)
(22,28)(24,30)(25,45)(27,47)(29,49)(31,38)(32,39)(34,41)(36,43)(40,55)(42,57)
(44,50)(46,51)(48,53)(52,61)(54,58)(56,59)(60,62);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(62)!(3,4)(5,6);
s1 := Sym(62)!(1,5)(2,3)(4,6);
s2 := Sym(62)!( 8, 9)(10,11)(12,15)(13,17)(14,16)(18,19)(20,25)(21,27)(22,26)
(23,29)(24,28)(30,31)(33,40)(34,39)(35,42)(36,41)(37,44)(38,43)(45,46)(47,52)
(48,51)(49,54)(50,53)(55,56)(57,60)(58,59)(61,62);
s3 := Sym(62)!( 7,13)( 8,10)( 9,21)(11,23)(12,16)(14,18)(15,33)(17,35)(19,37)
(20,26)(22,28)(24,30)(25,45)(27,47)(29,49)(31,38)(32,39)(34,41)(36,43)(40,55)
(42,57)(44,50)(46,51)(48,53)(52,61)(54,58)(56,59)(60,62);
poly := sub<Sym(62)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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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