Polytope of Type {2,17}

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

Permutation Representation (Magma) :

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

to this polytope