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Polytope of Type {20,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,15}*1440a
if this polytope has a name.
Group : SmallGroup(1440,4642)
Rank : 3
Schlafli Type : {20,15}
Number of vertices, edges, etc : 48, 360, 36
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
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 : {10,15}*720
   3-fold quotients : {20,5}*480
   4-fold quotients : {10,15}*360
   6-fold quotients : {10,5}*240
   12-fold quotients : {5,5}*120, {10,5}*120a, {10,5}*120b
   24-fold quotients : {5,5}*60
   120-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)(11,40)
(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)(28,32)
(33,48)(35,39)(41,47);;
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)
(50,51);;
s2 := ( 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)
(49,50);;
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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(51)!( 1, 4)( 2,34)( 3,45)( 5,43)( 6,27)( 7,25)( 8,30)( 9,36)(10,38)
(11,40)(12,37)(13,29)(14,42)(15,31)(16,23)(17,44)(18,24)(19,26)(20,21)(22,46)
(28,32)(33,48)(35,39)(41,47);
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)
(50,51);
s2 := 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)
(49,50);
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*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1 >; 
 
References : None.
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