Polytope of Type {2,2,6,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,28}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11517)
Rank : 5
Schlafli Type : {2,2,6,28}
Number of vertices, edges, etc : 2, 2, 6, 84, 28
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 : {2,2,6,14}*672
   3-fold quotients : {2,2,2,28}*448
   6-fold quotients : {2,2,2,14}*224
   7-fold quotients : {2,2,6,4}*192a
   12-fold quotients : {2,2,2,7}*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 := (12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(18,25)(33,40)(34,41)(35,42)
(36,43)(37,44)(38,45)(39,46)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67)
(75,82)(76,83)(77,84)(78,85)(79,86)(80,87)(81,88);;
s3 := ( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(20,25)(21,24)(22,23)
(26,33)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(41,46)(42,45)(43,44)(47,75)
(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,68)(55,74)(56,73)(57,72)(58,71)
(59,70)(60,69)(61,82)(62,88)(63,87)(64,86)(65,85)(66,84)(67,83);;
s4 := ( 5,48)( 6,47)( 7,53)( 8,52)( 9,51)(10,50)(11,49)(12,55)(13,54)(14,60)
(15,59)(16,58)(17,57)(18,56)(19,62)(20,61)(21,67)(22,66)(23,65)(24,64)(25,63)
(26,69)(27,68)(28,74)(29,73)(30,72)(31,71)(32,70)(33,76)(34,75)(35,81)(36,80)
(37,79)(38,78)(39,77)(40,83)(41,82)(42,88)(43,87)(44,86)(45,85)(46,84);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope