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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,42,4}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11661)
Rank : 5
Schlafli Type : {2,2,42,4}
Number of vertices, edges, etc : 2, 2, 42, 84, 4
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 : {2,2,42,2}*672
   3-fold quotients : {2,2,14,4}*448
   4-fold quotients : {2,2,21,2}*336
   6-fold quotients : {2,2,14,2}*224
   7-fold quotients : {2,2,6,4}*192a
   12-fold quotients : {2,2,7,2}*112
   14-fold quotients : {2,2,6,2}*96
   21-fold quotients : {2,2,2,4}*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 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)
(27,32)(28,31)(29,30)(33,40)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)(48,53)
(49,52)(50,51)(54,61)(55,67)(56,66)(57,65)(58,64)(59,63)(60,62)(69,74)(70,73)
(71,72)(75,82)(76,88)(77,87)(78,86)(79,85)(80,84)(81,83);;
s3 := ( 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)(47,76)
(48,75)(49,81)(50,80)(51,79)(52,78)(53,77)(54,69)(55,68)(56,74)(57,73)(58,72)
(59,71)(60,70)(61,83)(62,82)(63,88)(64,87)(65,86)(66,85)(67,84);;
s4 := ( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,56)
(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)
(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)(36,78)
(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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(88)!(1,2);
s1 := Sym(88)!(3,4);
s2 := Sym(88)!( 6,11)( 7,10)( 8, 9)(12,19)(13,25)(14,24)(15,23)(16,22)(17,21)
(18,20)(27,32)(28,31)(29,30)(33,40)(34,46)(35,45)(36,44)(37,43)(38,42)(39,41)
(48,53)(49,52)(50,51)(54,61)(55,67)(56,66)(57,65)(58,64)(59,63)(60,62)(69,74)
(70,73)(71,72)(75,82)(76,88)(77,87)(78,86)(79,85)(80,84)(81,83);
s3 := 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)
(47,76)(48,75)(49,81)(50,80)(51,79)(52,78)(53,77)(54,69)(55,68)(56,74)(57,73)
(58,72)(59,71)(60,70)(61,83)(62,82)(63,88)(64,87)(65,86)(66,85)(67,84);
s4 := Sym(88)!( 5,47)( 6,48)( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)
(14,56)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)
(25,67)(26,68)(27,69)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,77)
(36,78)(37,79)(38,80)(39,81)(40,82)(41,83)(42,84)(43,85)(44,86)(45,87)(46,88);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope