Polytope of Type {20,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240844)
Rank : 3
Schlafli Type : {20,8}
Number of vertices, edges, etc : 120, 480, 48
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {10,8}*960c, {20,4}*960c
   4-fold quotients : {5,8}*480, {10,4}*480c
   8-fold quotients : {5,4}*240, {10,4}*240a, {10,4}*240b
   16-fold quotients : {5,4}*120
   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 := ( 1,15)( 2, 4)( 3,14)( 5, 9)( 6,31)( 7,35)( 8,24)(11,30)(12,18)(13,20)
(17,25)(19,32)(21,39)(22,40)(23,26)(29,34)(33,36)(37,38)(42,44);;
s1 := ( 1, 4)( 2, 7)( 3,10)( 5,13)( 8,19)( 9,21)(11,25)(12,27)(14,29)(15,26)
(16,32)(17,20)(18,22)(23,33)(28,37)(30,39)(31,38)(35,36)(41,44)(42,43);;
s2 := ( 1, 3)( 2,11)( 4,30)( 5,37)( 6,22)( 8,24)( 9,38)(10,28)(12,39)(13,33)
(14,15)(16,27)(17,25)(18,21)(19,26)(20,36)(23,32)(29,34)(31,40);;
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope