Polytope of Type {4,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,51}*408
if this polytope has a name.
Group : SmallGroup(408,37)
Rank : 3
Schlafli Type : {4,51}
Number of vertices, edges, etc : 4, 102, 51
Order of s₀s₁s₂ : 51
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,51,2} of size 816
   {4,51,4} of size 1632
Vertex Figure Of :
   {2,4,51} of size 816
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,51}*816, {4,102}*816b, {4,102}*816c
   3-fold covers : {4,153}*1224
   4-fold covers : {4,204}*1632b, {4,204}*1632c, {8,51}*1632, {4,102}*1632
Permutation Representation (GAP) :

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