Polytope of Type {20,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,3}*480
if this polytope has a name.
Group : SmallGroup(480,959)
Rank : 3
Schlafli Type : {20,3}
Number of vertices, edges, etc : 80, 120, 12
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,3,2} of size 960
Vertex Figure Of :
   {2,20,3} of size 960
   {4,20,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,3}*240
   4-fold quotients : {5,3}*120, {10,3}*120a, {10,3}*120b
   8-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,6}*960d
   3-fold covers : {20,3}*1440a, {60,3}*1440
   4-fold covers : {20,6}*1920d, {20,12}*1920k, {20,12}*1920m
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope