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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,34,4}*1632
if this polytope has a name.
Group : SmallGroup(1632,1097)
Rank : 5
Schlafli Type : {3,2,34,4}
Number of vertices, edges, etc : 3, 3, 34, 68, 4
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 : {3,2,34,2}*816
   4-fold quotients : {3,2,17,2}*408
   17-fold quotients : {3,2,2,4}*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 := ( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(22,37)(23,36)
(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(39,54)(40,53)(41,52)(42,51)(43,50)
(44,49)(45,48)(46,47)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)
(63,64);;
s3 := ( 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)(38,56)(39,55)(40,71)(41,70)(42,69)
(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)
(54,57);;
s4 := ( 4,38)( 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);;
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*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(71)!(2,3);
s1 := Sym(71)!(1,2);
s2 := Sym(71)!( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(22,37)
(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(39,54)(40,53)(41,52)(42,51)
(43,50)(44,49)(45,48)(46,47)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)
(63,64);
s3 := 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)(38,56)(39,55)(40,71)(41,70)
(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)
(53,58)(54,57);
s4 := Sym(71)!( 4,38)( 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);
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*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