Polytope of Type {4,2,42,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,42,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11661)
Rank : 5
Schlafli Type : {4,2,42,2}
Number of vertices, edges, etc : 4, 4, 42, 42, 2
Order of s₀s₁s₂s₃s₄ : 84
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 : {4,2,21,2}*672, {2,2,42,2}*672
   3-fold quotients : {4,2,14,2}*448
   4-fold quotients : {2,2,21,2}*336
   6-fold quotients : {4,2,7,2}*224, {2,2,14,2}*224
   7-fold quotients : {4,2,6,2}*192
   12-fold quotients : {2,2,7,2}*112
   14-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   21-fold quotients : {4,2,2,2}*64
   28-fold quotients : {2,2,3,2}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)(25,26)
(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);;
s3 := ( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)(18,35)
(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);;
s4 := (47,48);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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)!(2,3);
s1 := Sym(48)!(1,2)(3,4);
s2 := Sym(48)!( 7, 8)( 9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,24)(22,23)
(25,26)(27,30)(28,29)(31,32)(33,36)(34,35)(37,38)(39,42)(40,41)(43,46)(44,45);
s3 := Sym(48)!( 5,21)( 6,15)( 7,13)( 8,23)( 9,11)(10,33)(12,17)(14,27)(16,25)
(18,35)(19,22)(20,43)(24,29)(26,39)(28,37)(30,45)(31,34)(32,44)(36,41)(38,40)
(42,46);
s4 := Sym(48)!(47,48);
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*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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