Polytope of Type {2,2,2,6,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,6,14}*1344
if this polytope has a name.
Group : SmallGroup(1344,11709)
Rank : 6
Schlafli Type : {2,2,2,6,14}
Number of vertices, edges, etc : 2, 2, 2, 6, 42, 14
Order of s₀s₁s₂s₃s₄s₅ : 42
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   3-fold quotients : {2,2,2,2,14}*448
   6-fold quotients : {2,2,2,2,7}*224
   7-fold quotients : {2,2,2,6,2}*192
   14-fold quotients : {2,2,2,3,2}*96
   21-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,63)(15,64)(16,65)
(17,66)(18,67)(19,68)(20,69)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)
(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,84)(36,85)(37,86)(38,87)
(39,88)(40,89)(41,90)(42,77)(43,78)(44,79)(45,80)(46,81)(47,82)(48,83);;
s4 := ( 7,56)( 8,62)( 9,61)(10,60)(11,59)(12,58)(13,57)(14,49)(15,55)(16,54)
(17,53)(18,52)(19,51)(20,50)(21,63)(22,69)(23,68)(24,67)(25,66)(26,65)(27,64)
(28,77)(29,83)(30,82)(31,81)(32,80)(33,79)(34,78)(35,70)(36,76)(37,75)(38,74)
(39,73)(40,72)(41,71)(42,84)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85);;
s5 := ( 7,29)( 8,28)( 9,34)(10,33)(11,32)(12,31)(13,30)(14,36)(15,35)(16,41)
(17,40)(18,39)(19,38)(20,37)(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)(27,44)
(49,71)(50,70)(51,76)(52,75)(53,74)(54,73)(55,72)(56,78)(57,77)(58,83)(59,82)
(60,81)(61,80)(62,79)(63,85)(64,84)(65,90)(66,89)(67,88)(68,87)(69,86);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(90)!(1,2);
s1 := Sym(90)!(3,4);
s2 := Sym(90)!(5,6);
s3 := Sym(90)!( 7,49)( 8,50)( 9,51)(10,52)(11,53)(12,54)(13,55)(14,63)(15,64)
(16,65)(17,66)(18,67)(19,68)(20,69)(21,56)(22,57)(23,58)(24,59)(25,60)(26,61)
(27,62)(28,70)(29,71)(30,72)(31,73)(32,74)(33,75)(34,76)(35,84)(36,85)(37,86)
(38,87)(39,88)(40,89)(41,90)(42,77)(43,78)(44,79)(45,80)(46,81)(47,82)(48,83);
s4 := Sym(90)!( 7,56)( 8,62)( 9,61)(10,60)(11,59)(12,58)(13,57)(14,49)(15,55)
(16,54)(17,53)(18,52)(19,51)(20,50)(21,63)(22,69)(23,68)(24,67)(25,66)(26,65)
(27,64)(28,77)(29,83)(30,82)(31,81)(32,80)(33,79)(34,78)(35,70)(36,76)(37,75)
(38,74)(39,73)(40,72)(41,71)(42,84)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85);
s5 := Sym(90)!( 7,29)( 8,28)( 9,34)(10,33)(11,32)(12,31)(13,30)(14,36)(15,35)
(16,41)(17,40)(18,39)(19,38)(20,37)(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)
(27,44)(49,71)(50,70)(51,76)(52,75)(53,74)(54,73)(55,72)(56,78)(57,77)(58,83)
(59,82)(60,81)(61,80)(62,79)(63,85)(64,84)(65,90)(66,89)(67,88)(68,87)(69,86);
poly := sub<Sym(90)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope