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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,28,2,2}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11517)
Rank : 5
Schlafli Type : {6,28,2,2}
Number of vertices, edges, etc : 6, 84, 28, 2, 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 : {6,14,2,2}*672
   3-fold quotients : {2,28,2,2}*448
   6-fold quotients : {2,14,2,2}*224
   7-fold quotients : {6,4,2,2}*192a
   12-fold quotients : {2,7,2,2}*112
   14-fold quotients : {6,2,2,2}*96
   21-fold quotients : {2,4,2,2}*64
   28-fold quotients : {3,2,2,2}*48
   42-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope