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Polytope of Type {17,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {17,2}*68
if this polytope has a name.
Group : SmallGroup(68,4)
Rank : 3
Schlafli Type : {17,2}
Number of vertices, edges, etc : 17, 17, 2
Order of s0s1s2 : 34
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {17,2,2} of size 136
   {17,2,3} of size 204
   {17,2,4} of size 272
   {17,2,5} of size 340
   {17,2,6} of size 408
   {17,2,7} of size 476
   {17,2,8} of size 544
   {17,2,9} of size 612
   {17,2,10} of size 680
   {17,2,11} of size 748
   {17,2,12} of size 816
   {17,2,13} of size 884
   {17,2,14} of size 952
   {17,2,15} of size 1020
   {17,2,16} of size 1088
   {17,2,17} of size 1156
   {17,2,18} of size 1224
   {17,2,19} of size 1292
   {17,2,20} of size 1360
   {17,2,21} of size 1428
   {17,2,22} of size 1496
   {17,2,23} of size 1564
   {17,2,24} of size 1632
   {17,2,25} of size 1700
   {17,2,26} of size 1768
   {17,2,27} of size 1836
   {17,2,28} of size 1904
   {17,2,29} of size 1972
Vertex Figure Of :
   {2,17,2} of size 136
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {34,2}*136
   3-fold covers : {51,2}*204
   4-fold covers : {68,2}*272, {34,4}*272
   5-fold covers : {85,2}*340
   6-fold covers : {34,6}*408, {102,2}*408
   7-fold covers : {119,2}*476
   8-fold covers : {68,4}*544, {136,2}*544, {34,8}*544
   9-fold covers : {153,2}*612, {51,6}*612
   10-fold covers : {34,10}*680, {170,2}*680
   11-fold covers : {187,2}*748
   12-fold covers : {34,12}*816, {68,6}*816a, {204,2}*816, {102,4}*816a, {51,6}*816, {51,4}*816
   13-fold covers : {221,2}*884
   14-fold covers : {34,14}*952, {238,2}*952
   15-fold covers : {255,2}*1020
   16-fold covers : {68,8}*1088a, {136,4}*1088a, {68,8}*1088b, {136,4}*1088b, {68,4}*1088, {34,16}*1088, {272,2}*1088
   17-fold covers : {289,2}*1156, {17,34}*1156
   18-fold covers : {34,18}*1224, {306,2}*1224, {102,6}*1224a, {102,6}*1224b, {102,6}*1224c
   19-fold covers : {323,2}*1292
   20-fold covers : {34,20}*1360, {68,10}*1360, {340,2}*1360, {170,4}*1360
   21-fold covers : {357,2}*1428
   22-fold covers : {34,22}*1496, {374,2}*1496
   23-fold covers : {391,2}*1564
   24-fold covers : {34,24}*1632, {136,6}*1632, {68,12}*1632, {204,4}*1632a, {408,2}*1632, {102,8}*1632, {51,12}*1632, {51,8}*1632, {68,6}*1632, {102,6}*1632, {102,4}*1632
   25-fold covers : {425,2}*1700, {85,10}*1700
   26-fold covers : {34,26}*1768, {442,2}*1768
   27-fold covers : {459,2}*1836, {153,6}*1836, {51,6}*1836
   28-fold covers : {34,28}*1904, {68,14}*1904, {476,2}*1904, {238,4}*1904
   29-fold covers : {493,2}*1972
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (18,19);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(19)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s1 := Sym(19)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(19)!(18,19);
poly := sub<Sym(19)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2, 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*s0*s1*s0*s1*s0*s1 >; 
 

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