Polytope of Type {12,2,7,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,7,2}*672
if this polytope has a name.
Group : SmallGroup(672,1140)
Rank : 5
Schlafli Type : {12,2,7,2}
Number of vertices, edges, etc : 12, 12, 7, 7, 2
Order of s₀s₁s₂s₃s₄ : 84
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,7,2,2} of size 1344
Vertex Figure Of :
   {2,12,2,7,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,7,2}*336
   3-fold quotients : {4,2,7,2}*224
   4-fold quotients : {3,2,7,2}*168
   6-fold quotients : {2,2,7,2}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,2,7,2}*1344, {12,2,14,2}*1344
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,15)(16,17)(18,19);;
s3 := (13,14)(15,16)(17,18);;
s4 := (20,21);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(21)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(21)!(14,15)(16,17)(18,19);
s3 := Sym(21)!(13,14)(15,16)(17,18);
s4 := Sym(21)!(20,21);
poly := sub<Sym(21)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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