Polytope of Type {3,2,14}

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

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

Permutation Representation (Magma) :

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

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