Polytope of Type {4,2,17}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,17}*272
if this polytope has a name.
Group : SmallGroup(272,40)
Rank : 4
Schlafli Type : {4,2,17}
Number of vertices, edges, etc : 4, 4, 17, 17
Order of s₀s₁s₂s₃ : 68
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,17,2} of size 544
Vertex Figure Of :
   {2,4,2,17} of size 544
   {3,4,2,17} of size 816
   {4,4,2,17} of size 1088
   {6,4,2,17} of size 1632
   {3,4,2,17} of size 1632
   {6,4,2,17} of size 1632
   {6,4,2,17} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,17}*136
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,17}*544, {4,2,34}*544
   3-fold covers : {12,2,17}*816, {4,2,51}*816
   4-fold covers : {16,2,17}*1088, {4,4,34}*1088, {4,2,68}*1088, {8,2,34}*1088
   5-fold covers : {20,2,17}*1360, {4,2,85}*1360
   6-fold covers : {24,2,17}*1632, {8,2,51}*1632, {12,2,34}*1632, {4,6,34}*1632a, {4,2,102}*1632
   7-fold covers : {28,2,17}*1904, {4,2,119}*1904
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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