Polytope of Type {68,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {68,2}*272
if this polytope has a name.
Group : SmallGroup(272,38)
Rank : 3
Schlafli Type : {68,2}
Number of vertices, edges, etc : 68, 68, 2
Order of s₀s₁s₂ : 68
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {68,2,2} of size 544
   {68,2,3} of size 816
   {68,2,4} of size 1088
   {68,2,5} of size 1360
   {68,2,6} of size 1632
   {68,2,7} of size 1904
Vertex Figure Of :
   {2,68,2} of size 544
   {4,68,2} of size 1088
   {6,68,2} of size 1632
   {6,68,2} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {34,2}*136
   4-fold quotients : {17,2}*68
   17-fold quotients : {4,2}*16
   34-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {68,4}*544, {136,2}*544
   3-fold covers : {68,6}*816a, {204,2}*816
   4-fold covers : {68,8}*1088a, {136,4}*1088a, {68,8}*1088b, {136,4}*1088b, {68,4}*1088, {272,2}*1088
   5-fold covers : {68,10}*1360, {340,2}*1360
   6-fold covers : {136,6}*1632, {68,12}*1632, {204,4}*1632a, {408,2}*1632
   7-fold covers : {68,14}*1904, {476,2}*1904
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope