Polytope of Type {14,7,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,7,2}*392
if this polytope has a name.
Group : SmallGroup(392,41)
Rank : 4
Schlafli Type : {14,7,2}
Number of vertices, edges, etc : 14, 49, 7, 2
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,7,2,2} of size 784
   {14,7,2,3} of size 1176
   {14,7,2,4} of size 1568
   {14,7,2,5} of size 1960
Vertex Figure Of :
   {2,14,7,2} of size 784
   {4,14,7,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,7,2}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {14,14,2}*784b
   3-fold covers : {14,21,2}*1176
   4-fold covers : {14,28,2}*1568b, {14,14,4}*1568b, {28,14,2}*1568c
   5-fold covers : {14,35,2}*1960
Permutation Representation (GAP) :

s0 := ( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)
(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);;
s1 := ( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(15,43)(16,49)(17,48)
(18,47)(19,46)(20,45)(21,44)(22,36)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)
(30,35)(31,34)(32,33);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)(14,45)
(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)(25,34)
(26,33)(27,32)(28,31);;
s3 := (50,51);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(51)!( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)
(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)
(28,35);
s1 := Sym(51)!( 1, 8)( 2,14)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(15,43)(16,49)
(17,48)(18,47)(19,46)(20,45)(21,44)(22,36)(23,42)(24,41)(25,40)(26,39)(27,38)
(28,37)(30,35)(31,34)(32,33);
s2 := Sym(51)!( 1, 2)( 3, 7)( 4, 6)( 8,44)( 9,43)(10,49)(11,48)(12,47)(13,46)
(14,45)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(22,30)(23,29)(24,35)
(25,34)(26,33)(27,32)(28,31);
s3 := Sym(51)!(50,51);
poly := sub<Sym(51)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

to this polytope