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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,2,7}*392
if this polytope has a name.
Group : SmallGroup(392,41)
Rank : 5
Schlafli Type : {7,2,2,7}
Number of vertices, edges, etc : 7, 7, 2, 7, 7
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,2,7,2} of size 784
Vertex Figure Of :
   {2,7,2,2,7} of size 784
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,2,14}*784, {14,2,2,7}*784
   3-fold covers : {7,2,2,21}*1176, {21,2,2,7}*1176
   4-fold covers : {7,2,2,28}*1568, {28,2,2,7}*1568, {7,2,4,14}*1568, {14,4,2,7}*1568, {14,2,2,14}*1568
   5-fold covers : {7,2,2,35}*1960, {35,2,2,7}*1960
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (8,9);;
s3 := (11,12)(13,14)(15,16);;
s4 := (10,11)(12,13)(14,15);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!(2,3)(4,5)(6,7);
s1 := Sym(16)!(1,2)(3,4)(5,6);
s2 := Sym(16)!(8,9);
s3 := Sym(16)!(11,12)(13,14)(15,16);
s4 := Sym(16)!(10,11)(12,13)(14,15);
poly := sub<Sym(16)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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