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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,34,4}*1088
if this polytope has a name.
Group : SmallGroup(1088,1369)
Rank : 5
Schlafli Type : {2,2,34,4}
Number of vertices, edges, etc : 2, 2, 34, 68, 4
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 : {2,2,34,2}*544
   4-fold quotients : {2,2,17,2}*272
   17-fold quotients : {2,2,2,4}*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 := ( 6,21)( 7,20)( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(23,38)(24,37)
(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(40,55)(41,54)(42,53)(43,52)(44,51)
(45,50)(46,49)(47,48)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)
(64,65);;
s3 := ( 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)(39,57)(40,56)(41,72)(42,71)(43,70)
(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)
(55,58);;
s4 := ( 5,39)( 6,40)( 7,41)( 8,42)( 9,43)(10,44)(11,45)(12,46)(13,47)(14,48)
(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)(25,59)
(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)
(37,71)(38,72);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(72)!(1,2);
s1 := Sym(72)!(3,4);
s2 := Sym(72)!( 6,21)( 7,20)( 8,19)( 9,18)(10,17)(11,16)(12,15)(13,14)(23,38)
(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)(40,55)(41,54)(42,53)(43,52)
(44,51)(45,50)(46,49)(47,48)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)
(64,65);
s3 := 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)(39,57)(40,56)(41,72)(42,71)
(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)
(54,59)(55,58);
s4 := Sym(72)!( 5,39)( 6,40)( 7,41)( 8,42)( 9,43)(10,44)(11,45)(12,46)(13,47)
(14,48)(15,49)(16,50)(17,51)(18,52)(19,53)(20,54)(21,55)(22,56)(23,57)(24,58)
(25,59)(26,60)(27,61)(28,62)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)
(36,70)(37,71)(38,72);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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