Polytope of Type {12,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,7}*336
if this polytope has a name.
Group : SmallGroup(336,148)
Rank : 4
Schlafli Type : {12,2,7}
Number of vertices, edges, etc : 12, 12, 7, 7
Order of s₀s₁s₂s₃ : 84
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,7,2} of size 672
Vertex Figure Of :
   {2,12,2,7} of size 672
   {4,12,2,7} of size 1344
   {4,12,2,7} of size 1344
   {4,12,2,7} of size 1344
   {3,12,2,7} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,7}*168
   3-fold quotients : {4,2,7}*112
   4-fold quotients : {3,2,7}*84
   6-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,2,7}*672, {12,2,14}*672
   3-fold covers : {36,2,7}*1008, {12,2,21}*1008
   4-fold covers : {48,2,7}*1344, {12,2,28}*1344, {12,4,14}*1344, {24,2,14}*1344
   5-fold covers : {60,2,7}*1680, {12,2,35}*1680
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);;
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, 
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(19)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(19)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(19)!(14,15)(16,17)(18,19);
s3 := Sym(19)!(13,14)(15,16)(17,18);
poly := sub<Sym(19)|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, 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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