Polytope of Type {2,14,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,7}*392
if this polytope has a name.
Group : SmallGroup(392,41)
Rank : 4
Schlafli Type : {2,14,7}
Number of vertices, edges, etc : 2, 14, 49, 7
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,7,2} of size 784
Vertex Figure Of :
   {2,2,14,7} of size 784
   {3,2,14,7} of size 1176
   {4,2,14,7} of size 1568
   {5,2,14,7} of size 1960
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,14,7}*784, {2,14,14}*784b
   3-fold covers : {6,14,7}*1176, {2,14,21}*1176
   4-fold covers : {8,14,7}*1568, {2,14,28}*1568b, {4,14,14}*1568c, {2,28,14}*1568c
   5-fold covers : {10,14,7}*1960, {2,14,35}*1960
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope