Polytope of Type {20,4,2}

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

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

Permutation Representation (Magma) :

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

to this polytope