Polytope of Type {5,2,7,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,7,14}*1960
if this polytope has a name.
Group : SmallGroup(1960,126)
Rank : 5
Schlafli Type : {5,2,7,14}
Number of vertices, edges, etc : 5, 5, 7, 49, 14
Order of s₀s₁s₂s₃s₄ : 70
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {5,2,7,2}*280
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope