Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240558)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 160, 480, 40
Order of s0s1s2 : 24
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*960a, {24,6}*960b, {12,6}*960b
   4-fold quotients : {12,6}*480a, {12,6}*480b, {6,6}*480
   8-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   16-fold quotients : {6,6}*120
   60-fold quotients : {8,2}*32
   120-fold quotients : {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(18,21)(19,20);;
s1 := ( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(17,20);;
s2 := ( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,19)(20,21);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 1,16)( 2, 9)( 3, 8)( 4,14)( 5,12)( 6,13)( 7,15)(10,11)(18,21)
(19,20);
s1 := Sym(21)!( 1, 7)( 2, 6)( 3,15)( 4,10)( 5,13)( 8,14)( 9,11)(12,16)(17,20);
s2 := Sym(21)!( 1,16)( 2,14)( 3,13)( 4, 9)( 5,15)( 6, 8)( 7,12)(10,11)(18,19)
(20,21);
poly := sub<Sym(21)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0 >; 
 
References : None.
to this polytope