Polytope of Type {6,2,50}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,50}*1200
if this polytope has a name.
Group : SmallGroup(1200,203)
Rank : 4
Schlafli Type : {6,2,50}
Number of vertices, edges, etc : 6, 6, 50, 50
Order of s₀s₁s₂s₃ : 150
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {3,2,50}*600, {6,2,25}*600
   3-fold quotients : {2,2,50}*400
   4-fold quotients : {3,2,25}*300
   5-fold quotients : {6,2,10}*240
   6-fold quotients : {2,2,25}*200
   10-fold quotients : {3,2,10}*120, {6,2,5}*120
   15-fold quotients : {2,2,10}*80
   20-fold quotients : {3,2,5}*60
   25-fold quotients : {6,2,2}*48
   30-fold quotients : {2,2,5}*40
   50-fold quotients : {3,2,2}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)
(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)
(51,52)(53,54)(55,56);;
s3 := ( 7,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)(22,27)(24,25)
(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,43)(40,41)(42,47)(44,45)(46,51)
(48,49)(50,55)(52,53)(54,56);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(56)!(3,4)(5,6);
s1 := Sym(56)!(1,5)(2,3)(4,6);
s2 := Sym(56)!( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)
(49,50)(51,52)(53,54)(55,56);
s3 := Sym(56)!( 7,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)(22,27)
(24,25)(26,31)(28,29)(30,35)(32,33)(34,39)(36,37)(38,43)(40,41)(42,47)(44,45)
(46,51)(48,49)(50,55)(52,53)(54,56);
poly := sub<Sym(56)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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