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Polytope of Type {56,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,2,6}*1344
if this polytope has a name.
Group : SmallGroup(1344,8483)
Rank : 4
Schlafli Type : {56,2,6}
Number of vertices, edges, etc : 56, 56, 6, 6
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 : {56,2,3}*672, {28,2,6}*672
   3-fold quotients : {56,2,2}*448
   4-fold quotients : {28,2,3}*336, {14,2,6}*336
   6-fold quotients : {28,2,2}*224
   7-fold quotients : {8,2,6}*192
   8-fold quotients : {7,2,6}*168, {14,2,3}*168
   12-fold quotients : {14,2,2}*112
   14-fold quotients : {8,2,3}*96, {4,2,6}*96
   16-fold quotients : {7,2,3}*84
   21-fold quotients : {8,2,2}*64
   24-fold quotients : {7,2,2}*56
   28-fold quotients : {4,2,3}*48, {2,2,6}*48
   42-fold quotients : {4,2,2}*32
   56-fold quotients : {2,2,3}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)
(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)(42,45)
(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)(14,20)
(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)(36,51)
(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);;
s2 := (59,60)(61,62);;
s3 := (57,61)(58,59)(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, 
s2*s3*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)
(17,23)(18,22)(24,25)(27,34)(28,33)(29,36)(30,35)(31,38)(32,37)(39,40)(41,46)
(42,45)(43,48)(44,47)(49,50)(51,54)(52,53)(55,56);
s1 := Sym(62)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,27)(11,29)(13,31)
(14,20)(16,22)(18,24)(19,39)(21,41)(23,43)(25,32)(26,33)(28,35)(30,37)(34,49)
(36,51)(38,44)(40,45)(42,47)(46,55)(48,52)(50,53)(54,56);
s2 := Sym(62)!(59,60)(61,62);
s3 := Sym(62)!(57,61)(58,59)(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, s2*s3*s2*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 >; 
 

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