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Polytope of Type {7,2,3,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,3,2,2}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 6
Schlafli Type : {7,2,3,2,2}
Number of vertices, edges, etc : 7, 7, 3, 3, 2, 2
Order of s0s1s2s3s4s5 : 42
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,3,2,2,2} of size 672
   {7,2,3,2,2,3} of size 1008
   {7,2,3,2,2,4} of size 1344
   {7,2,3,2,2,5} of size 1680
Vertex Figure Of :
   {2,7,2,3,2,2} of size 672
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,3,2,4}*672, {7,2,6,2,2}*672, {14,2,3,2,2}*672
   3-fold covers : {7,2,9,2,2}*1008, {7,2,3,2,6}*1008, {7,2,3,6,2}*1008, {21,2,3,2,2}*1008
   4-fold covers : {7,2,3,2,8}*1344, {7,2,12,2,2}*1344, {28,2,3,2,2}*1344, {7,2,6,2,4}*1344, {7,2,6,4,2}*1344a, {14,2,3,2,4}*1344, {7,2,3,4,2}*1344, {14,2,6,2,2}*1344
   5-fold covers : {7,2,3,2,10}*1680, {7,2,15,2,2}*1680, {35,2,3,2,2}*1680
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10);;
s3 := (8,9);;
s4 := (11,12);;
s5 := (13,14);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(2,3)(4,5)(6,7);
s1 := Sym(14)!(1,2)(3,4)(5,6);
s2 := Sym(14)!( 9,10);
s3 := Sym(14)!(8,9);
s4 := Sym(14)!(11,12);
s5 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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