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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,14,7}*1568
if this polytope has a name.
Group : SmallGroup(1568,925)
Rank : 6
Schlafli Type : {2,2,2,14,7}
Number of vertices, edges, etc : 2, 2, 2, 14, 49, 7
Order of s₀s₁s₂s₃s₄s₅ : 14
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,2,2,2,7}*224
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,42)(22,43)(23,44)
(24,45)(25,46)(26,47)(27,48)(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)
(34,41);;
s4 := ( 7,14)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(21,49)(22,55)(23,54)
(24,53)(25,52)(26,51)(27,50)(28,42)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)
(36,41)(37,40)(38,39);;
s5 := ( 7, 8)( 9,13)(10,12)(14,50)(15,49)(16,55)(17,54)(18,53)(19,52)(20,51)
(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)(27,44)(28,36)(29,35)(30,41)(31,40)
(32,39)(33,38)(34,37);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(55)!(1,2);
s1 := Sym(55)!(3,4);
s2 := Sym(55)!(5,6);
s3 := Sym(55)!(14,49)(15,50)(16,51)(17,52)(18,53)(19,54)(20,55)(21,42)(22,43)
(23,44)(24,45)(25,46)(26,47)(27,48)(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)
(34,41);
s4 := Sym(55)!( 7,14)( 8,20)( 9,19)(10,18)(11,17)(12,16)(13,15)(21,49)(22,55)
(23,54)(24,53)(25,52)(26,51)(27,50)(28,42)(29,48)(30,47)(31,46)(32,45)(33,44)
(34,43)(36,41)(37,40)(38,39);
s5 := Sym(55)!( 7, 8)( 9,13)(10,12)(14,50)(15,49)(16,55)(17,54)(18,53)(19,52)
(20,51)(21,43)(22,42)(23,48)(24,47)(25,46)(26,45)(27,44)(28,36)(29,35)(30,41)
(31,40)(32,39)(33,38)(34,37);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s5*s3*s4*s3*s4*s5*s3*s4*s3*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope