Polytope of Type {2,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,42}*336
if this polytope has a name.
Group : SmallGroup(336,227)
Rank : 4
Schlafli Type : {2,2,42}
Number of vertices, edges, etc : 2, 2, 42, 42
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,42,2} of size 672
   {2,2,42,4} of size 1344
   {2,2,42,4} of size 1344
   {2,2,42,4} of size 1344
Vertex Figure Of :
   {2,2,2,42} of size 672
   {3,2,2,42} of size 1008
   {4,2,2,42} of size 1344
   {5,2,2,42} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,21}*168
   3-fold quotients : {2,2,14}*112
   6-fold quotients : {2,2,7}*56
   7-fold quotients : {2,2,6}*48
   14-fold quotients : {2,2,3}*24
   21-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,84}*672, {2,4,42}*672a, {4,2,42}*672
   3-fold covers : {2,2,126}*1008, {2,6,42}*1008b, {2,6,42}*1008c, {6,2,42}*1008
   4-fold covers : {2,4,84}*1344a, {4,2,84}*1344, {4,4,42}*1344, {2,2,168}*1344, {2,8,42}*1344, {8,2,42}*1344, {2,4,42}*1344
   5-fold covers : {2,10,42}*1680, {10,2,42}*1680, {2,2,210}*1680
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26)
(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);;
s3 := ( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)(18,35)
(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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(46)!(1,2);
s1 := Sym(46)!(3,4);
s2 := Sym(46)!( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)
(25,26)(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);
s3 := Sym(46)!( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)
(18,35)(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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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