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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,6,2}*1344
if this polytope has a name.
Group : SmallGroup(1344,11709)
Rank : 6
Schlafli Type : {2,2,14,6,2}
Number of vertices, edges, etc : 2, 2, 14, 42, 6, 2
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 : {2,2,14,2,2}*448
   6-fold quotients : {2,2,7,2,2}*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 := ( 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)(48,53)(49,52)(50,51)
(55,60)(56,59)(57,58)(62,67)(63,66)(64,65)(69,74)(70,73)(71,72)(76,81)(77,80)
(78,79)(83,88)(84,87)(85,86);;
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 := ( 5,75)( 6,76)( 7,77)( 8,78)( 9,79)(10,80)(11,81)(12,68)(13,69)(14,70)
(15,71)(16,72)(17,73)(18,74)(19,82)(20,83)(21,84)(22,85)(23,86)(24,87)(25,88)
(26,54)(27,55)(28,56)(29,57)(30,58)(31,59)(32,60)(33,47)(34,48)(35,49)(36,50)
(37,51)(38,52)(39,53)(40,61)(41,62)(42,63)(43,64)(44,65)(45,66)(46,67);;
s5 := (89,90);;
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, 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, 
s4*s5*s4*s5, 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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope