Polytope of Type {2,2,4,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,51}*1632
if this polytope has a name.
Group : SmallGroup(1632,1200)
Rank : 5
Schlafli Type : {2,2,4,51}
Number of vertices, edges, etc : 2, 2, 4, 102, 51
Order of s₀s₁s₂s₃s₄ : 102
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   17-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 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)
(69,71)(70,72);;
s3 := ( 6, 7)( 9,69)(10,71)(11,70)(12,72)(13,65)(14,67)(15,66)(16,68)(17,61)
(18,63)(19,62)(20,64)(21,57)(22,59)(23,58)(24,60)(25,53)(26,55)(27,54)(28,56)
(29,49)(30,51)(31,50)(32,52)(33,45)(34,47)(35,46)(36,48)(37,41)(38,43)(39,42)
(40,44);;
s4 := ( 5, 9)( 6,12)( 7,11)( 8,10)(13,69)(14,72)(15,71)(16,70)(17,65)(18,68)
(19,67)(20,66)(21,61)(22,64)(23,63)(24,62)(25,57)(26,60)(27,59)(28,58)(29,53)
(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46)
(42,44);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(72)!(1,2);
s1 := Sym(72)!(3,4);
s2 := Sym(72)!( 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)(69,71)(70,72);
s3 := Sym(72)!( 6, 7)( 9,69)(10,71)(11,70)(12,72)(13,65)(14,67)(15,66)(16,68)
(17,61)(18,63)(19,62)(20,64)(21,57)(22,59)(23,58)(24,60)(25,53)(26,55)(27,54)
(28,56)(29,49)(30,51)(31,50)(32,52)(33,45)(34,47)(35,46)(36,48)(37,41)(38,43)
(39,42)(40,44);
s4 := Sym(72)!( 5, 9)( 6,12)( 7,11)( 8,10)(13,69)(14,72)(15,71)(16,70)(17,65)
(18,68)(19,67)(20,66)(21,61)(22,64)(23,63)(24,62)(25,57)(26,60)(27,59)(28,58)
(29,53)(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)
(40,46)(42,44);
poly := sub<Sym(72)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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