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Polytope of Type {2,6,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,7}*336
if this polytope has a name.
Group : SmallGroup(336,219)
Rank : 5
Schlafli Type : {2,6,2,7}
Number of vertices, edges, etc : 2, 6, 6, 7, 7
Order of s0s1s2s3s4 : 42
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,7,2} of size 672
Vertex Figure Of :
   {2,2,6,2,7} of size 672
   {3,2,6,2,7} of size 1008
   {4,2,6,2,7} of size 1344
   {5,2,6,2,7} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,7}*168
   3-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,2,7}*672, {4,6,2,7}*672a, {2,6,2,14}*672
   3-fold covers : {2,18,2,7}*1008, {6,6,2,7}*1008a, {6,6,2,7}*1008b, {2,6,2,21}*1008
   4-fold covers : {4,12,2,7}*1344a, {2,24,2,7}*1344, {8,6,2,7}*1344, {2,12,2,14}*1344, {2,6,2,28}*1344, {2,6,4,14}*1344, {4,6,2,14}*1344a, {4,6,2,7}*1344
   5-fold covers : {10,6,2,7}*1680, {2,30,2,7}*1680, {2,6,2,35}*1680
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := (10,11)(12,13)(14,15);;
s4 := ( 9,10)(11,12)(13,14);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!(1,2);
s1 := Sym(15)!(5,6)(7,8);
s2 := Sym(15)!(3,7)(4,5)(6,8);
s3 := Sym(15)!(10,11)(12,13)(14,15);
s4 := Sym(15)!( 9,10)(11,12)(13,14);
poly := sub<Sym(15)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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