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Polytope of Type {17,2,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {17,2,2,2}*272
if this polytope has a name.
Group : SmallGroup(272,53)
Rank : 5
Schlafli Type : {17,2,2,2}
Number of vertices, edges, etc : 17, 17, 2, 2, 2
Order of s0s1s2s3s4 : 34
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {17,2,2,2,2} of size 544
   {17,2,2,2,3} of size 816
   {17,2,2,2,4} of size 1088
   {17,2,2,2,5} of size 1360
   {17,2,2,2,6} of size 1632
   {17,2,2,2,7} of size 1904
Vertex Figure Of :
   {2,17,2,2,2} of size 544
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {17,2,2,4}*544, {17,2,4,2}*544, {34,2,2,2}*544
   3-fold covers : {17,2,2,6}*816, {17,2,6,2}*816, {51,2,2,2}*816
   4-fold covers : {17,2,4,4}*1088, {17,2,2,8}*1088, {17,2,8,2}*1088, {34,2,2,4}*1088, {34,2,4,2}*1088, {34,4,2,2}*1088, {68,2,2,2}*1088
   5-fold covers : {17,2,2,10}*1360, {17,2,10,2}*1360, {85,2,2,2}*1360
   6-fold covers : {17,2,2,12}*1632, {17,2,12,2}*1632, {17,2,4,6}*1632a, {17,2,6,4}*1632a, {51,2,2,4}*1632, {51,2,4,2}*1632, {34,2,2,6}*1632, {34,2,6,2}*1632, {34,6,2,2}*1632, {102,2,2,2}*1632
   7-fold covers : {17,2,2,14}*1904, {17,2,14,2}*1904, {119,2,2,2}*1904
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);;
s3 := (20,21);;
s4 := (22,23);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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(23)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);
s1 := Sym(23)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(23)!(18,19);
s3 := Sym(23)!(20,21);
s4 := Sym(23)!(22,23);
poly := sub<Sym(23)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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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