Polytope of Type {5,2,14,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,14,6}*1680
if this polytope has a name.
Group : SmallGroup(1680,966)
Rank : 5
Schlafli Type : {5,2,14,6}
Number of vertices, edges, etc : 5, 5, 14, 42, 6
Order of s₀s₁s₂s₃s₄ : 210
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) :
   3-fold quotients : {5,2,14,2}*560
   6-fold quotients : {5,2,7,2}*280
   7-fold quotients : {5,2,2,6}*240
   14-fold quotients : {5,2,2,3}*120
   21-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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