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Polytope of Type {7,2,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,8,2}*448
if this polytope has a name.
Group : SmallGroup(448,1207)
Rank : 5
Schlafli Type : {7,2,8,2}
Number of vertices, edges, etc : 7, 7, 8, 8, 2
Order of s0s1s2s3s4 : 56
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,8,2,2} of size 896
   {7,2,8,2,3} of size 1344
   {7,2,8,2,4} of size 1792
Vertex Figure Of :
   {2,7,2,8,2} of size 896
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,4,2}*224
   4-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,8,4}*896a, {7,2,16,2}*896, {14,2,8,2}*896
   3-fold covers : {7,2,24,2}*1344, {7,2,8,6}*1344, {21,2,8,2}*1344
   4-fold covers : {7,2,8,4}*1792a, {7,2,8,8}*1792b, {7,2,8,8}*1792c, {7,2,16,4}*1792a, {7,2,16,4}*1792b, {7,2,32,2}*1792, {14,2,8,4}*1792a, {14,4,8,2}*1792a, {28,2,8,2}*1792, {14,2,16,2}*1792
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,14);;
s3 := ( 8, 9)(10,11)(12,13)(14,15);;
s4 := (16,17);;
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*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(17)!(2,3)(4,5)(6,7);
s1 := Sym(17)!(1,2)(3,4)(5,6);
s2 := Sym(17)!( 9,10)(11,12)(13,14);
s3 := Sym(17)!( 8, 9)(10,11)(12,13)(14,15);
s4 := Sym(17)!(16,17);
poly := sub<Sym(17)|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*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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