Polytope of Type {2,34,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34,2}*272
if this polytope has a name.
Group : SmallGroup(272,53)
Rank : 4
Schlafli Type : {2,34,2}
Number of vertices, edges, etc : 2, 34, 34, 2
Order of s₀s₁s₂s₃ : 34
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,34,2,2} of size 544
   {2,34,2,3} of size 816
   {2,34,2,4} of size 1088
   {2,34,2,5} of size 1360
   {2,34,2,6} of size 1632
   {2,34,2,7} of size 1904
Vertex Figure Of :
   {2,2,34,2} of size 544
   {3,2,34,2} of size 816
   {4,2,34,2} of size 1088
   {5,2,34,2} of size 1360
   {6,2,34,2} of size 1632
   {7,2,34,2} of size 1904
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,17,2}*136
   17-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,68,2}*544, {2,34,4}*544, {4,34,2}*544
   3-fold covers : {2,34,6}*816, {6,34,2}*816, {2,102,2}*816
   4-fold covers : {2,68,4}*1088, {4,68,2}*1088, {4,34,4}*1088, {2,34,8}*1088, {8,34,2}*1088, {2,136,2}*1088
   5-fold covers : {2,34,10}*1360, {10,34,2}*1360, {2,170,2}*1360
   6-fold covers : {2,34,12}*1632, {12,34,2}*1632, {2,68,6}*1632a, {6,68,2}*1632a, {4,34,6}*1632, {6,34,4}*1632, {2,204,2}*1632, {2,102,4}*1632a, {4,102,2}*1632a
   7-fold covers : {2,34,14}*1904, {14,34,2}*1904, {2,238,2}*1904
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,36);;
s3 := (37,38);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(38)!(1,2);
s1 := Sym(38)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);
s2 := Sym(38)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,27)(24,25)(26,31)(28,29)(30,35)(32,33)(34,36);
s3 := Sym(38)!(37,38);
poly := sub<Sym(38)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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