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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,17}*272
if this polytope has a name.
Group : SmallGroup(272,53)
Rank : 5
Schlafli Type : {2,2,2,17}
Number of vertices, edges, etc : 2, 2, 2, 17, 17
Order of s₀s₁s₂s₃s₄ : 34
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,17,2} of size 544
Vertex Figure Of :
   {2,2,2,2,17} of size 544
   {3,2,2,2,17} of size 816
   {4,2,2,2,17} of size 1088
   {5,2,2,2,17} of size 1360
   {6,2,2,2,17} of size 1632
   {7,2,2,2,17} of size 1904
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,2,17}*544, {4,2,2,17}*544, {2,2,2,34}*544
   3-fold covers : {2,6,2,17}*816, {6,2,2,17}*816, {2,2,2,51}*816
   4-fold covers : {4,4,2,17}*1088, {2,8,2,17}*1088, {8,2,2,17}*1088, {2,2,4,34}*1088, {2,4,2,34}*1088, {4,2,2,34}*1088, {2,2,2,68}*1088
   5-fold covers : {2,10,2,17}*1360, {10,2,2,17}*1360, {2,2,2,85}*1360
   6-fold covers : {2,12,2,17}*1632, {12,2,2,17}*1632, {4,6,2,17}*1632a, {6,4,2,17}*1632a, {2,4,2,51}*1632, {4,2,2,51}*1632, {2,2,6,34}*1632, {2,6,2,34}*1632, {6,2,2,34}*1632, {2,2,2,102}*1632
   7-fold covers : {2,14,2,17}*1904, {14,2,2,17}*1904, {2,2,2,119}*1904
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);;
s4 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);;
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*s1*s0*s1, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(23)!(1,2);
s1 := Sym(23)!(3,4);
s2 := Sym(23)!(5,6);
s3 := Sym(23)!( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);
s4 := Sym(23)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);
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*s1*s0*s1, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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