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Polytope of Type {9,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,42}*1512
if this polytope has a name.
Group : SmallGroup(1512,560)
Rank : 4
Schlafli Type : {9,2,42}
Number of vertices, edges, etc : 9, 9, 42, 42
Order of s₀s₁s₂s₃ : 126
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 : {9,2,21}*756
   3-fold quotients : {9,2,14}*504, {3,2,42}*504
   6-fold quotients : {9,2,7}*252, {3,2,21}*252
   7-fold quotients : {9,2,6}*216
   9-fold quotients : {3,2,14}*168
   14-fold quotients : {9,2,3}*108
   18-fold quotients : {3,2,7}*84
   21-fold quotients : {9,2,2}*72, {3,2,6}*72
   42-fold quotients : {3,2,3}*36
   63-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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