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Polytope of Type {2,4,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,51}*816
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 4
Schlafli Type : {2,4,51}
Number of vertices, edges, etc : 2, 4, 102, 51
Order of s0s1s2s3 : 102
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,51,2} of size 1632
Vertex Figure Of :
   {2,2,4,51} of size 1632
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,51}*1632, {2,4,102}*1632b, {2,4,102}*1632c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)
(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)
(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62)(63,65)(64,66)
(67,69)(68,70);;
s2 := ( 4, 5)( 7,67)( 8,69)( 9,68)(10,70)(11,63)(12,65)(13,64)(14,66)(15,59)
(16,61)(17,60)(18,62)(19,55)(20,57)(21,56)(22,58)(23,51)(24,53)(25,52)(26,54)
(27,47)(28,49)(29,48)(30,50)(31,43)(32,45)(33,44)(34,46)(35,39)(36,41)(37,40)
(38,42);;
s3 := ( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,67)(12,70)(13,69)(14,68)(15,63)(16,66)
(17,65)(18,64)(19,59)(20,62)(21,61)(22,60)(23,55)(24,58)(25,57)(26,56)(27,51)
(28,54)(29,53)(30,52)(31,47)(32,50)(33,49)(34,48)(35,43)(36,46)(37,45)(38,44)
(40,42);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
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*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(70)!(1,2);
s1 := Sym(70)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)
(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)
(43,45)(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62)(63,65)
(64,66)(67,69)(68,70);
s2 := Sym(70)!( 4, 5)( 7,67)( 8,69)( 9,68)(10,70)(11,63)(12,65)(13,64)(14,66)
(15,59)(16,61)(17,60)(18,62)(19,55)(20,57)(21,56)(22,58)(23,51)(24,53)(25,52)
(26,54)(27,47)(28,49)(29,48)(30,50)(31,43)(32,45)(33,44)(34,46)(35,39)(36,41)
(37,40)(38,42);
s3 := Sym(70)!( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,67)(12,70)(13,69)(14,68)(15,63)
(16,66)(17,65)(18,64)(19,59)(20,62)(21,61)(22,60)(23,55)(24,58)(25,57)(26,56)
(27,51)(28,54)(29,53)(30,52)(31,47)(32,50)(33,49)(34,48)(35,43)(36,46)(37,45)
(38,44)(40,42);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, 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*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 >; 
 

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