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

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

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

Permutation Representation (Magma) :

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

to this polytope