Polytope of Type {6,2,2,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,34}*1632
if this polytope has a name.
Group : SmallGroup(1632,1207)
Rank : 5
Schlafli Type : {6,2,2,34}
Number of vertices, edges, etc : 6, 6, 2, 34, 34
Order of s0s1s2s3s4 : 102
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,34}*816, {6,2,2,17}*816
   3-fold quotients : {2,2,2,34}*544
   4-fold quotients : {3,2,2,17}*408
   6-fold quotients : {2,2,2,17}*272
   17-fold quotients : {6,2,2,2}*96
   34-fold quotients : {3,2,2,2}*48
   51-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := (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)(37,38)(39,40)(41,42);;
s4 := ( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,29)(26,27)
(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,42);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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(42)!(3,4)(5,6);
s1 := Sym(42)!(1,5)(2,3)(4,6);
s2 := Sym(42)!(7,8);
s3 := Sym(42)!(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)(37,38)(39,40)(41,42);
s4 := Sym(42)!( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,29)
(26,27)(28,33)(30,31)(32,37)(34,35)(36,41)(38,39)(40,42);
poly := sub<Sym(42)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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 >; 
 

to this polytope