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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,42}*672
if this polytope has a name.
Group : SmallGroup(672,1279)
Rank : 5
Schlafli Type : {2,2,2,42}
Number of vertices, edges, etc : 2, 2, 2, 42, 42
Order of s₀s₁s₂s₃s₄ : 42
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,42,2} of size 1344
Vertex Figure Of :
   {2,2,2,2,42} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,2,21}*336
   3-fold quotients : {2,2,2,14}*224
   6-fold quotients : {2,2,2,7}*112
   7-fold quotients : {2,2,2,6}*96
   14-fold quotients : {2,2,2,3}*48
   21-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,2,84}*1344, {2,2,4,42}*1344a, {2,4,2,42}*1344, {4,2,2,42}*1344
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 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);;
s4 := ( 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,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, s1*s2*s1*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, 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(48)!(1,2);
s1 := Sym(48)!(3,4);
s2 := Sym(48)!(5,6);
s3 := 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);
s4 := 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,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, 
s1*s2*s1*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, 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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