Polytope of Type {7,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,7}*196
if this polytope has a name.
Group : SmallGroup(196,9)
Rank : 4
Schlafli Type : {7,2,7}
Number of vertices, edges, etc : 7, 7, 7, 7
Order of s₀s₁s₂s₃ : 7
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,7,2} of size 392
Vertex Figure Of :
   {2,7,2,7} of size 392
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,14}*392, {14,2,7}*392
   3-fold covers : {7,2,21}*588, {21,2,7}*588
   4-fold covers : {7,2,28}*784, {28,2,7}*784, {14,2,14}*784
   5-fold covers : {7,2,35}*980, {35,2,7}*980
   6-fold covers : {7,2,42}*1176, {14,2,21}*1176, {21,2,14}*1176, {42,2,7}*1176
   7-fold covers : {7,2,49}*1372, {49,2,7}*1372, {7,14,7}*1372
   8-fold covers : {7,2,56}*1568, {56,2,7}*1568, {14,2,28}*1568, {28,2,14}*1568, {14,4,14}*1568
   9-fold covers : {7,2,63}*1764, {63,2,7}*1764, {21,2,21}*1764
   10-fold covers : {7,2,70}*1960, {14,2,35}*1960, {35,2,14}*1960, {70,2,7}*1960
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);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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 ];;
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)(11,12)(13,14);
s3 := Sym(14)!( 8, 9)(10,11)(12,13);
poly := sub<Sym(14)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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 >;

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