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

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

to this polytope