Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 24, 240, 120
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   2-fold quotients : {2,4,10}*960b
   4-fold quotients : {2,4,10}*480b
   8-fold quotients : {2,4,5}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope