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Polytope of Type {42,2,2}

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

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