Polytope of Type {2,4,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,34}*544
if this polytope has a name.
Group : SmallGroup(544,225)
Rank : 4
Schlafli Type : {2,4,34}
Number of vertices, edges, etc : 2, 4, 68, 34
Order of s₀s₁s₂s₃ : 68
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,34,2} of size 1088
Vertex Figure Of :
   {2,2,4,34} of size 1088
   {3,2,4,34} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,34}*272
   4-fold quotients : {2,2,17}*136
   17-fold quotients : {2,4,2}*32
   34-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,34}*1088, {2,4,68}*1088, {2,8,34}*1088
   3-fold covers : {2,12,34}*1632, {6,4,34}*1632, {2,4,102}*1632a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (37,54)(38,55)(39,56)(40,57)(41,58)(42,59)(43,60)(44,61)(45,62)(46,63)
(47,64)(48,65)(49,66)(50,67)(51,68)(52,69)(53,70);;
s2 := ( 3,37)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)(10,47)(11,46)(12,45)
(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,54)(21,70)(22,69)(23,68)
(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)
(35,56)(36,55);;
s3 := ( 3, 4)( 5,19)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(20,21)(22,36)
(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,38)(39,53)(40,52)(41,51)(42,50)
(43,49)(44,48)(45,47)(54,55)(56,70)(57,69)(58,68)(59,67)(60,66)(61,65)
(62,64);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
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*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(70)!(1,2);
s1 := Sym(70)!(37,54)(38,55)(39,56)(40,57)(41,58)(42,59)(43,60)(44,61)(45,62)
(46,63)(47,64)(48,65)(49,66)(50,67)(51,68)(52,69)(53,70);
s2 := Sym(70)!( 3,37)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)(10,47)(11,46)
(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,54)(21,70)(22,69)
(23,68)(24,67)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)
(34,57)(35,56)(36,55);
s3 := Sym(70)!( 3, 4)( 5,19)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(20,21)
(22,36)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30)(37,38)(39,53)(40,52)(41,51)
(42,50)(43,49)(44,48)(45,47)(54,55)(56,70)(57,69)(58,68)(59,67)(60,66)(61,65)
(62,64);
poly := sub<Sym(70)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, 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*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 >;

to this polytope