Polytope of Type {6,2,42}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,42}*1008
if this polytope has a name.
Group : SmallGroup(1008,942)
Rank : 4
Schlafli Type : {6,2,42}
Number of vertices, edges, etc : 6, 6, 42, 42
Order of s₀s₁s₂s₃ : 42
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 : {3,2,42}*504, {6,2,21}*504
   3-fold quotients : {6,2,14}*336, {2,2,42}*336
   4-fold quotients : {3,2,21}*252
   6-fold quotients : {3,2,14}*168, {6,2,7}*168, {2,2,21}*168
   7-fold quotients : {6,2,6}*144
   9-fold quotients : {2,2,14}*112
   12-fold quotients : {3,2,7}*84
   14-fold quotients : {3,2,6}*72, {6,2,3}*72
   18-fold quotients : {2,2,7}*56
   21-fold quotients : {2,2,6}*48, {6,2,2}*48
   28-fold quotients : {3,2,3}*36
   42-fold quotients : {2,2,3}*24, {3,2,2}*24
   63-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)(17,20)(18,19)(21,22)(23,26)(24,25)(27,28)
(29,32)(30,31)(33,34)(35,38)(36,37)(39,40)(41,44)(42,43)(45,48)(46,47);;
s3 := ( 7,23)( 8,17)( 9,15)(10,25)(11,13)(12,35)(14,19)(16,29)(18,27)(20,37)
(21,24)(22,45)(26,31)(28,41)(30,39)(32,47)(33,36)(34,46)(38,43)(40,42)
(44,48);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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