Polytope of Type {2,17,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,17,2}*136
if this polytope has a name.
Group : SmallGroup(136,14)
Rank : 4
Schlafli Type : {2,17,2}
Number of vertices, edges, etc : 2, 17, 17, 2
Order of s₀s₁s₂s₃ : 34
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,17,2,2} of size 272
   {2,17,2,3} of size 408
   {2,17,2,4} of size 544
   {2,17,2,5} of size 680
   {2,17,2,6} of size 816
   {2,17,2,7} of size 952
   {2,17,2,8} of size 1088
   {2,17,2,9} of size 1224
   {2,17,2,10} of size 1360
   {2,17,2,11} of size 1496
   {2,17,2,12} of size 1632
   {2,17,2,13} of size 1768
   {2,17,2,14} of size 1904
Vertex Figure Of :
   {2,2,17,2} of size 272
   {3,2,17,2} of size 408
   {4,2,17,2} of size 544
   {5,2,17,2} of size 680
   {6,2,17,2} of size 816
   {7,2,17,2} of size 952
   {8,2,17,2} of size 1088
   {9,2,17,2} of size 1224
   {10,2,17,2} of size 1360
   {11,2,17,2} of size 1496
   {12,2,17,2} of size 1632
   {13,2,17,2} of size 1768
   {14,2,17,2} of size 1904
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,34,2}*272
   3-fold covers : {2,51,2}*408
   4-fold covers : {2,68,2}*544, {2,34,4}*544, {4,34,2}*544
   5-fold covers : {2,85,2}*680
   6-fold covers : {2,34,6}*816, {6,34,2}*816, {2,102,2}*816
   7-fold covers : {2,119,2}*952
   8-fold covers : {2,68,4}*1088, {4,68,2}*1088, {4,34,4}*1088, {2,34,8}*1088, {8,34,2}*1088, {2,136,2}*1088
   9-fold covers : {2,153,2}*1224, {2,51,6}*1224, {6,51,2}*1224
   10-fold covers : {2,34,10}*1360, {10,34,2}*1360, {2,170,2}*1360
   11-fold covers : {2,187,2}*1496
   12-fold covers : {2,34,12}*1632, {12,34,2}*1632, {2,68,6}*1632a, {6,68,2}*1632a, {4,34,6}*1632, {6,34,4}*1632, {2,204,2}*1632, {2,102,4}*1632a, {4,102,2}*1632a, {2,51,6}*1632, {6,51,2}*1632, {2,51,4}*1632, {4,51,2}*1632
   13-fold covers : {2,221,2}*1768
   14-fold covers : {2,34,14}*1904, {14,34,2}*1904, {2,238,2}*1904
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope