Polytope of Type {2,3,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,42}*1008
if this polytope has a name.
Group : SmallGroup(1008,942)
Rank : 5
Schlafli Type : {2,3,2,42}
Number of vertices, edges, etc : 2, 3, 3, 42, 42
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,3,2,21}*504
   3-fold quotients : {2,3,2,14}*336
   6-fold quotients : {2,3,2,7}*168
   7-fold quotients : {2,3,2,6}*144
   14-fold quotients : {2,3,2,3}*72
   21-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 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);;
s4 := ( 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,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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 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(47)!(1,2);
s1 := Sym(47)!(4,5);
s2 := Sym(47)!(3,4);
s3 := 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);
s4 := 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,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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, 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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