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Polytope of Type {2,42,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,42,2}*336
if this polytope has a name.
Group : SmallGroup(336,227)
Rank : 4
Schlafli Type : {2,42,2}
Number of vertices, edges, etc : 2, 42, 42, 2
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,42,2,2} of size 672
   {2,42,2,3} of size 1008
   {2,42,2,4} of size 1344
   {2,42,2,5} of size 1680
Vertex Figure Of :
   {2,2,42,2} of size 672
   {3,2,42,2} of size 1008
   {4,2,42,2} of size 1344
   {5,2,42,2} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,21,2}*168
   3-fold quotients : {2,14,2}*112
   6-fold quotients : {2,7,2}*56
   7-fold quotients : {2,6,2}*48
   14-fold quotients : {2,3,2}*24
   21-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,84,2}*672, {2,42,4}*672a, {4,42,2}*672a
   3-fold covers : {2,126,2}*1008, {2,42,6}*1008b, {2,42,6}*1008c, {6,42,2}*1008b, {6,42,2}*1008c
   4-fold covers : {2,84,4}*1344a, {4,84,2}*1344a, {4,42,4}*1344a, {2,168,2}*1344, {2,42,8}*1344, {8,42,2}*1344, {2,42,4}*1344, {4,42,2}*1344
   5-fold covers : {2,42,10}*1680, {10,42,2}*1680, {2,210,2}*1680
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,18)(19,22)(20,21)(23,24)
(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,44)(42,43);;
s2 := ( 3,19)( 4,13)( 5,11)( 6,21)( 7, 9)( 8,31)(10,15)(12,25)(14,23)(16,33)
(17,20)(18,41)(22,27)(24,37)(26,35)(28,43)(29,32)(30,42)(34,39)(36,38)
(40,44);;
s3 := (45,46);;
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, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(46)!(1,2);
s1 := Sym(46)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,18)(19,22)(20,21)
(23,24)(25,28)(26,27)(29,30)(31,34)(32,33)(35,36)(37,40)(38,39)(41,44)(42,43);
s2 := Sym(46)!( 3,19)( 4,13)( 5,11)( 6,21)( 7, 9)( 8,31)(10,15)(12,25)(14,23)
(16,33)(17,20)(18,41)(22,27)(24,37)(26,35)(28,43)(29,32)(30,42)(34,39)(36,38)
(40,44);
s3 := Sym(46)!(45,46);
poly := sub<Sym(46)|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, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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