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

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

s0 := (1,2);;
s1 := (3,4);;
s2 := (47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)(56,77)
(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)
(67,88);;
s3 := ( 5,47)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,61)(13,67)(14,66)
(15,65)(16,64)(17,63)(18,62)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)(25,55)
(26,68)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,82)(34,88)(35,87)(36,86)
(37,85)(38,84)(39,83)(40,75)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76);;
s4 := ( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)(22,24)
(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)(47,55)
(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66)(68,76)(69,75)
(70,81)(71,80)(72,79)(73,78)(74,77)(82,83)(84,88)(85,87);;
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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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(88)!(1,2);
s1 := Sym(88)!(3,4);
s2 := Sym(88)!(47,68)(48,69)(49,70)(50,71)(51,72)(52,73)(53,74)(54,75)(55,76)
(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)
(67,88);
s3 := Sym(88)!( 5,47)( 6,53)( 7,52)( 8,51)( 9,50)(10,49)(11,48)(12,61)(13,67)
(14,66)(15,65)(16,64)(17,63)(18,62)(19,54)(20,60)(21,59)(22,58)(23,57)(24,56)
(25,55)(26,68)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,82)(34,88)(35,87)
(36,86)(37,85)(38,84)(39,83)(40,75)(41,81)(42,80)(43,79)(44,78)(45,77)(46,76);
s4 := Sym(88)!( 5,13)( 6,12)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(19,20)(21,25)
(22,24)(26,34)(27,33)(28,39)(29,38)(30,37)(31,36)(32,35)(40,41)(42,46)(43,45)
(47,55)(48,54)(49,60)(50,59)(51,58)(52,57)(53,56)(61,62)(63,67)(64,66)(68,76)
(69,75)(70,81)(71,80)(72,79)(73,78)(74,77)(82,83)(84,88)(85,87);
poly := sub<Sym(88)|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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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 >;

to this polytope