Polytope of Type {14,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,3}*168
if this polytope has a name.
Group : SmallGroup(168,50)
Rank : 4
Schlafli Type : {14,2,3}
Number of vertices, edges, etc : 14, 14, 3, 3
Order of s₀s₁s₂s₃ : 42
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,2,3,2} of size 336
   {14,2,3,3} of size 672
   {14,2,3,4} of size 672
   {14,2,3,6} of size 1008
   {14,2,3,4} of size 1344
   {14,2,3,6} of size 1344
   {14,2,3,5} of size 1680
Vertex Figure Of :
   {2,14,2,3} of size 336
   {4,14,2,3} of size 672
   {6,14,2,3} of size 1008
   {7,14,2,3} of size 1176
   {8,14,2,3} of size 1344
   {10,14,2,3} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {7,2,3}*84
   7-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,2,3}*336, {14,2,6}*336
   3-fold covers : {14,2,9}*504, {14,6,3}*504, {42,2,3}*504
   4-fold covers : {56,2,3}*672, {14,2,12}*672, {28,2,6}*672, {14,4,6}*672, {14,4,3}*672
   5-fold covers : {14,2,15}*840, {70,2,3}*840
   6-fold covers : {28,2,9}*1008, {14,2,18}*1008, {28,6,3}*1008, {84,2,3}*1008, {14,6,6}*1008a, {14,6,6}*1008b, {42,2,6}*1008
   7-fold covers : {98,2,3}*1176, {14,2,21}*1176
   8-fold covers : {112,2,3}*1344, {28,2,12}*1344, {14,4,12}*1344, {28,4,6}*1344, {14,2,24}*1344, {56,2,6}*1344, {14,8,6}*1344, {28,4,3}*1344, {14,8,3}*1344, {14,4,6}*1344
   9-fold covers : {14,2,27}*1512, {14,6,9}*1512, {14,6,3}*1512, {126,2,3}*1512, {42,2,9}*1512, {42,6,3}*1512a, {42,6,3}*1512b
   10-fold covers : {28,2,15}*1680, {140,2,3}*1680, {14,10,6}*1680, {14,2,30}*1680, {70,2,6}*1680
   11-fold covers : {14,2,33}*1848, {154,2,3}*1848
Permutation Representation (GAP) :

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