Polytope of Type {5,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,12}*480
if this polytope has a name.
Group : SmallGroup(480,959)
Rank : 3
Schlafli Type : {5,12}
Number of vertices, edges, etc : 20, 120, 48
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,12,2} of size 960
   {5,12,4} of size 1920
Vertex Figure Of :
   {2,5,12} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6}*240b
   4-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c
   8-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,12}*960d
   3-fold covers : {15,12}*1440a, {15,12}*1440b
   4-fold covers : {10,12}*1920c, {20,12}*1920l, {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 := ( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)(13,25)
(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);;
s2 := ( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)(12,33)
(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)(34,43)
(37,39)(41,48)(42,45);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*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)!( 2, 3)( 4,17)( 5,19)( 7,28)( 8,35)( 9,29)(10,15)(11,26)(12,39)
(13,25)(14,27)(20,38)(21,33)(22,44)(23,31)(24,30)(32,42)(34,41)(40,43)(45,47);
s2 := Sym(48)!( 1, 8)( 2,17)( 3,29)( 4,10)( 5,26)( 6,25)( 7,36)( 9,16)(11,35)
(12,33)(13,30)(14,15)(18,27)(19,24)(20,40)(21,38)(22,47)(23,46)(28,32)(31,44)
(34,43)(37,39)(41,48)(42,45);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1 >;

References : None.
to this polytope