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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,28,2}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11517)
Rank : 5
Schlafli Type : {2,6,28,2}
Number of vertices, edges, etc : 2, 6, 84, 28, 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 : {2,6,14,2}*672
   3-fold quotients : {2,2,28,2}*448
   6-fold quotients : {2,2,14,2}*224
   7-fold quotients : {2,6,4,2}*192a
   12-fold quotients : {2,2,7,2}*112
   14-fold quotients : {2,6,2,2}*96
   21-fold quotients : {2,2,4,2}*64
   28-fold quotients : {2,3,2,2}*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 := (10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(31,38)(32,39)(33,40)
(34,41)(35,42)(36,43)(37,44)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)(58,65)
(73,80)(74,81)(75,82)(76,83)(77,84)(78,85)(79,86);;
s2 := ( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)(20,21)
(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)(45,73)
(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,66)(53,72)(54,71)(55,70)(56,69)
(57,68)(58,67)(59,80)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81);;
s3 := ( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,53)(11,52)(12,58)
(13,57)(14,56)(15,55)(16,54)(17,60)(18,59)(19,65)(20,64)(21,63)(22,62)(23,61)
(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,74)(32,73)(33,79)(34,78)
(35,77)(36,76)(37,75)(38,81)(39,80)(40,86)(41,85)(42,84)(43,83)(44,82);;
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*s1*s0*s1, 
s0*s2*s0*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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(31,38)(32,39)
(33,40)(34,41)(35,42)(36,43)(37,44)(52,59)(53,60)(54,61)(55,62)(56,63)(57,64)
(58,65)(73,80)(74,81)(75,82)(76,83)(77,84)(78,85)(79,86);
s2 := Sym(88)!( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)
(20,21)(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)
(45,73)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,66)(53,72)(54,71)(55,70)
(56,69)(57,68)(58,67)(59,80)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81);
s3 := Sym(88)!( 3,46)( 4,45)( 5,51)( 6,50)( 7,49)( 8,48)( 9,47)(10,53)(11,52)
(12,58)(13,57)(14,56)(15,55)(16,54)(17,60)(18,59)(19,65)(20,64)(21,63)(22,62)
(23,61)(24,67)(25,66)(26,72)(27,71)(28,70)(29,69)(30,68)(31,74)(32,73)(33,79)
(34,78)(35,77)(36,76)(37,75)(38,81)(39,80)(40,86)(41,85)(42,84)(43,83)(44,82);
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*s1*s0*s1, s0*s2*s0*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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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