Polytope of Type {5,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,42}*840
if this polytope has a name.
Group : SmallGroup(840,173)
Rank : 4
Schlafli Type : {5,2,42}
Number of vertices, edges, etc : 5, 5, 42, 42
Order of s₀s₁s₂s₃ : 210
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,42,2} of size 1680
Vertex Figure Of :
   {2,5,2,42} of size 1680
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,21}*420
   3-fold quotients : {5,2,14}*280
   6-fold quotients : {5,2,7}*140
   7-fold quotients : {5,2,6}*120
   14-fold quotients : {5,2,3}*60
   21-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,84}*1680, {10,2,42}*1680
Permutation Representation (GAP) :

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