Polytope of Type {3,2,4,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,34}*1632
if this polytope has a name.
Group : SmallGroup(1632,1097)
Rank : 5
Schlafli Type : {3,2,4,34}
Number of vertices, edges, etc : 3, 3, 4, 68, 34
Order of s₀s₁s₂s₃s₄ : 204
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
   4-fold quotients : {3,2,2,17}*408
   17-fold quotients : {3,2,4,2}*96
   34-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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