Polytope of Type {4,34,2}

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

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

to this polytope