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

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

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

Permutation Representation (Magma) :

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

to this polytope