Polytope of Type {2,2,4,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,34}*1088
if this polytope has a name.
Group : SmallGroup(1088,1369)
Rank : 5
Schlafli Type : {2,2,4,34}
Number of vertices, edges, etc : 2, 2, 4, 68, 34
Order of s₀s₁s₂s₃s₄ : 68
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 : {2,2,2,34}*544
   4-fold quotients : {2,2,2,17}*272
   17-fold quotients : {2,2,4,2}*64
   34-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (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)(54,71)(55,72);;
s3 := ( 5,39)( 6,55)( 7,54)( 8,53)( 9,52)(10,51)(11,50)(12,49)(13,48)(14,47)
(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,56)(23,72)(24,71)(25,70)
(26,69)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)
(37,58)(38,57);;
s4 := ( 5, 6)( 7,21)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(22,23)(24,38)
(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,40)(41,55)(42,54)(43,53)(44,52)
(45,51)(46,50)(47,49)(56,57)(58,72)(59,71)(60,70)(61,69)(62,68)(63,67)
(64,66);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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(72)!(1,2);
s1 := Sym(72)!(3,4);
s2 := Sym(72)!(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)(54,71)(55,72);
s3 := Sym(72)!( 5,39)( 6,55)( 7,54)( 8,53)( 9,52)(10,51)(11,50)(12,49)(13,48)
(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,56)(23,72)(24,71)
(25,70)(26,69)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)
(36,59)(37,58)(38,57);
s4 := Sym(72)!( 5, 6)( 7,21)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(22,23)
(24,38)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,40)(41,55)(42,54)(43,53)
(44,52)(45,51)(46,50)(47,49)(56,57)(58,72)(59,71)(60,70)(61,69)(62,68)(63,67)
(64,66);
poly := sub<Sym(72)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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