Polytope of Type {2,2,14,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,14,7}*784
if this polytope has a name.
Group : SmallGroup(784,169)
Rank : 5
Schlafli Type : {2,2,14,7}
Number of vertices, edges, etc : 2, 2, 14, 49, 7
Order of s₀s₁s₂s₃s₄ : 14
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,14,7,2} of size 1568
Vertex Figure Of :
   {2,2,2,14,7} of size 1568
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,2,2,7}*112
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,14,7}*1568, {2,4,14,7}*1568, {2,2,14,14}*1568b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,40)(20,41)(21,42)
(22,43)(23,44)(24,45)(25,46)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)
(32,39);;
s3 := ( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,47)(20,53)(21,52)
(22,51)(23,50)(24,49)(25,48)(26,40)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)
(34,39)(35,38)(36,37);;
s4 := ( 5, 6)( 7,11)( 8,10)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)(18,49)
(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)(25,42)(26,34)(27,33)(28,39)(29,38)
(30,37)(31,36)(32,35);;
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*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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(53)!(1,2);
s1 := Sym(53)!(3,4);
s2 := Sym(53)!(12,47)(13,48)(14,49)(15,50)(16,51)(17,52)(18,53)(19,40)(20,41)
(21,42)(22,43)(23,44)(24,45)(25,46)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)
(32,39);
s3 := Sym(53)!( 5,12)( 6,18)( 7,17)( 8,16)( 9,15)(10,14)(11,13)(19,47)(20,53)
(21,52)(22,51)(23,50)(24,49)(25,48)(26,40)(27,46)(28,45)(29,44)(30,43)(31,42)
(32,41)(34,39)(35,38)(36,37);
s4 := Sym(53)!( 5, 6)( 7,11)( 8,10)(12,48)(13,47)(14,53)(15,52)(16,51)(17,50)
(18,49)(19,41)(20,40)(21,46)(22,45)(23,44)(24,43)(25,42)(26,34)(27,33)(28,39)
(29,38)(30,37)(31,36)(32,35);
poly := sub<Sym(53)|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*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, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope