Polytope of Type {6,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24,2}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240809)
Rank : 4
Schlafli Type : {6,24,2}
Number of vertices, edges, etc : 20, 240, 80, 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 : {6,12,2}*960b
   4-fold quotients : {6,6,2}*480a
   8-fold quotients : {6,6,2}*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, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)(12,27)
(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)(31,44)
(32,38)(40,42)(45,46);;
s2 := ( 1,16)( 2,32)( 3,13)( 4, 6)( 5, 7)( 8,42)( 9,44)(10,19)(11,24)(12,23)
(14,27)(15,33)(17,35)(18,34)(20,37)(21,40)(22,25)(26,41)(28,30)(29,36)(31,39)
(38,45)(43,47)(46,48);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
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, 6)( 2,28)( 3,36)( 4,26)( 5,14)( 7,41)( 8,37)( 9,18)(10,11)
(12,27)(13,48)(15,16)(17,25)(19,39)(20,47)(21,34)(22,33)(23,24)(29,43)(30,35)
(31,44)(32,38)(40,42)(45,46);
s2 := Sym(50)!( 1,16)( 2,32)( 3,13)( 4, 6)( 5, 7)( 8,42)( 9,44)(10,19)(11,24)
(12,23)(14,27)(15,33)(17,35)(18,34)(20,37)(21,40)(22,25)(26,41)(28,30)(29,36)
(31,39)(38,45)(43,47)(46,48);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

to this polytope