Polytope of Type {15,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,12}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {15,12}
Number of vertices, edges, etc : 60, 360, 48
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 60
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,6}*720d
   3-fold quotients : {5,12}*480
   4-fold quotients : {15,3}*360
   6-fold quotients : {5,6}*240b
   12-fold quotients : {5,3}*120, {5,6}*120b, {5,6}*120c
   24-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)
(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);;
s1 := ( 2,23)( 3,39)( 4,33)( 5,17)( 6, 7)( 8,20)( 9,22)(10,34)(11,29)(12,16)
(13,24)(14,26)(15,41)(18,32)(19,48)(25,44)(27,38)(36,40)(42,46)(43,47)
(49,50);;
s2 := ( 1, 4)( 2,35)( 3, 5)( 6,25)( 7,27)( 8,29)( 9,46)(10,24)(11,47)(12,37)
(13,30)(14,23)(15,31)(16,42)(17,48)(18,38)(19,21)(20,26)(22,36)(28,32)(33,44)
(34,39)(40,41)(43,45)(50,51);;
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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(51)!( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)
(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)
(50,51);
s1 := Sym(51)!( 2,23)( 3,39)( 4,33)( 5,17)( 6, 7)( 8,20)( 9,22)(10,34)(11,29)
(12,16)(13,24)(14,26)(15,41)(18,32)(19,48)(25,44)(27,38)(36,40)(42,46)(43,47)
(49,50);
s2 := Sym(51)!( 1, 4)( 2,35)( 3, 5)( 6,25)( 7,27)( 8,29)( 9,46)(10,24)(11,47)
(12,37)(13,30)(14,23)(15,31)(16,42)(17,48)(18,38)(19,21)(20,26)(22,36)(28,32)
(33,44)(34,39)(40,41)(43,45)(50,51);
poly := sub<Sym(51)|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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1 >;

References : None.
to this polytope