Polytope of Type {2,7,14}

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

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

Permutation Representation (Magma) :

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

to this polytope