Polytope of Type {17,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {17,2,3}*204
if this polytope has a name.
Group : SmallGroup(204,7)
Rank : 4
Schlafli Type : {17,2,3}
Number of vertices, edges, etc : 17, 17, 3, 3
Order of s₀s₁s₂s₃ : 51
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {17,2,3,2} of size 408
   {17,2,3,3} of size 816
   {17,2,3,4} of size 816
   {17,2,3,6} of size 1224
   {17,2,3,4} of size 1632
   {17,2,3,6} of size 1632
Vertex Figure Of :
   {2,17,2,3} of size 408
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {17,2,6}*408, {34,2,3}*408
   3-fold covers : {17,2,9}*612, {51,2,3}*612
   4-fold covers : {17,2,12}*816, {68,2,3}*816, {34,2,6}*816
   5-fold covers : {17,2,15}*1020, {85,2,3}*1020
   6-fold covers : {17,2,18}*1224, {34,2,9}*1224, {34,6,3}*1224, {51,2,6}*1224, {102,2,3}*1224
   7-fold covers : {17,2,21}*1428, {119,2,3}*1428
   8-fold covers : {17,2,24}*1632, {136,2,3}*1632, {34,2,12}*1632, {68,2,6}*1632, {34,4,6}*1632, {34,4,3}*1632
   9-fold covers : {17,2,27}*1836, {153,2,3}*1836, {51,2,9}*1836, {51,6,3}*1836
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 := (19,20);;
s3 := (18,19);;
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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope