Polytope of Type {51,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {51,4,2}*816
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 4
Schlafli Type : {51,4,2}
Number of vertices, edges, etc : 51, 102, 4, 2
Order of s₀s₁s₂s₃ : 102
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {51,4,2,2} of size 1632
Vertex Figure Of :
   {2,51,4,2} of size 1632
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {51,4,2}*1632, {102,4,2}*1632b, {102,4,2}*1632c
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*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