Polytope of Type {2,2,17}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,17}*136
if this polytope has a name.
Group : SmallGroup(136,14)
Rank : 4
Schlafli Type : {2,2,17}
Number of vertices, edges, etc : 2, 2, 17, 17
Order of s₀s₁s₂s₃ : 34
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,17,2} of size 272
Vertex Figure Of :
   {2,2,2,17} of size 272
   {3,2,2,17} of size 408
   {4,2,2,17} of size 544
   {5,2,2,17} of size 680
   {6,2,2,17} of size 816
   {7,2,2,17} of size 952
   {8,2,2,17} of size 1088
   {9,2,2,17} of size 1224
   {10,2,2,17} of size 1360
   {11,2,2,17} of size 1496
   {12,2,2,17} of size 1632
   {13,2,2,17} of size 1768
   {14,2,2,17} of size 1904
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,17}*272, {2,2,34}*272
   3-fold covers : {6,2,17}*408, {2,2,51}*408
   4-fold covers : {8,2,17}*544, {2,2,68}*544, {2,4,34}*544, {4,2,34}*544
   5-fold covers : {10,2,17}*680, {2,2,85}*680
   6-fold covers : {12,2,17}*816, {4,2,51}*816, {2,6,34}*816, {6,2,34}*816, {2,2,102}*816
   7-fold covers : {14,2,17}*952, {2,2,119}*952
   8-fold covers : {16,2,17}*1088, {4,4,34}*1088, {2,4,68}*1088, {4,2,68}*1088, {2,8,34}*1088, {8,2,34}*1088, {2,2,136}*1088
   9-fold covers : {18,2,17}*1224, {2,2,153}*1224, {2,6,51}*1224, {6,2,51}*1224
   10-fold covers : {20,2,17}*1360, {4,2,85}*1360, {2,10,34}*1360, {10,2,34}*1360, {2,2,170}*1360
   11-fold covers : {22,2,17}*1496, {2,2,187}*1496
   12-fold covers : {24,2,17}*1632, {8,2,51}*1632, {2,12,34}*1632, {12,2,34}*1632, {2,6,68}*1632a, {6,2,68}*1632, {4,6,34}*1632a, {6,4,34}*1632, {2,2,204}*1632, {2,4,102}*1632a, {4,2,102}*1632, {2,6,51}*1632, {2,4,51}*1632
   13-fold covers : {26,2,17}*1768, {2,2,221}*1768
   14-fold covers : {28,2,17}*1904, {4,2,119}*1904, {2,14,34}*1904, {14,2,34}*1904, {2,2,238}*1904
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(21)!(1,2);
s1 := Sym(21)!(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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

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