Polytope of Type {7,2,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,4,3}*336
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 5
Schlafli Type : {7,2,4,3}
Number of vertices, edges, etc : 7, 7, 4, 6, 3
Order of s₀s₁s₂s₃s₄ : 21
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,4,3,2} of size 672
   {7,2,4,3,4} of size 1344
Vertex Figure Of :
   {2,7,2,4,3} of size 672
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,4,3}*672, {7,2,4,6}*672b, {7,2,4,6}*672c, {14,2,4,3}*672
   3-fold covers : {7,2,4,9}*1008, {21,2,4,3}*1008
   4-fold covers : {7,2,4,12}*1344b, {7,2,4,12}*1344c, {28,2,4,3}*1344, {7,2,8,3}*1344, {7,2,4,6}*1344, {14,2,4,3}*1344, {14,2,4,6}*1344b, {14,2,4,6}*1344c
   5-fold covers : {7,2,4,15}*1680, {35,2,4,3}*1680
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 8, 9)(10,11);;
s3 := ( 9,10);;
s4 := (10,11);;
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*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(2,3)(4,5)(6,7);
s1 := Sym(11)!(1,2)(3,4)(5,6);
s2 := Sym(11)!( 8, 9)(10,11);
s3 := Sym(11)!( 9,10);
s4 := Sym(11)!(10,11);
poly := sub<Sym(11)|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*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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