Questions?
See the FAQ
or other info.

Polytope of Type {40,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240561)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s0s1s2 : 40
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 : {40,6}*960a, {40,6}*960b, {20,6}*960c
   4-fold quotients : {20,6}*480a, {20,6}*480b, {10,6}*480c
   8-fold quotients : {5,6}*240b, {10,3}*240, {10,6}*240c, {10,6}*240d, {10,6}*240e, {10,6}*240f
   16-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c, {10,3}*120a, {10,3}*120b
   32-fold quotients : {5,3}*60
   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 := ( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12)(18,21)(19,20);;
s1 := ( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,20)(19,21);;
s2 := ( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,20)(19,21);;
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 1,11)( 2, 9)( 3,15)( 4,13)( 5, 7)( 6,16)( 8,14)(10,12)(18,21)
(19,20);
s1 := Sym(21)!( 1, 3)( 2, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,20)
(19,21);
s2 := Sym(21)!( 1, 2)( 3, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(18,20)
(19,21);
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, 
s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope