Polytope of Type {4,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,34}*272
Also Known As : {4,34|2}. if this polytope has another name.
Group : SmallGroup(272,40)
Rank : 3
Schlafli Type : {4,34}
Number of vertices, edges, etc : 4, 68, 34
Order of s₀s₁s₂ : 68
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,34,2} of size 544
   {4,34,4} of size 1088
   {4,34,6} of size 1632
Vertex Figure Of :
   {2,4,34} of size 544
   {4,4,34} of size 1088
   {6,4,34} of size 1632
   {3,4,34} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,34}*136
   4-fold quotients : {2,17}*68
   17-fold quotients : {4,2}*16
   34-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,68}*544, {8,34}*544
   3-fold covers : {12,34}*816, {4,102}*816a
   4-fold covers : {8,68}*1088a, {4,136}*1088a, {8,68}*1088b, {4,136}*1088b, {4,68}*1088, {16,34}*1088
   5-fold covers : {20,34}*1360, {4,170}*1360
   6-fold covers : {24,34}*1632, {12,68}*1632, {4,204}*1632a, {8,102}*1632
   7-fold covers : {28,34}*1904, {4,238}*1904
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(68)!(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(68)!( 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(68)!( 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);
poly := sub<Sym(68)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References : None.
to this polytope