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Polytope of Type {3,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,20}*480
if this polytope has a name.
Group : SmallGroup(480,959)
Rank : 3
Schlafli Type : {3,20}
Number of vertices, edges, etc : 12, 120, 80
Order of s0s1s2 : 20
Order of s0s1s2s1 : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,20,2} of size 960
   {3,20,4} of size 1920
Vertex Figure Of :
   {2,3,20} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,10}*240
   4-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b
   8-fold quotients : {3,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*960d
   3-fold covers : {3,20}*1440a, {3,60}*1440
   4-fold covers : {6,20}*1920d, {12,20}*1920l, {12,20}*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, 3)( 2,23)( 4,35)( 5,29)( 6,15)( 7,10)( 8,21)( 9,22)(11,18)(13,17)
(14,19)(16,30)(20,38)(24,41)(25,40)(26,39)(27,42)(32,44)(33,43)(45,47);;
s2 := ( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)(12,29)
(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)(36,38)
(37,47)(41,42)(45,48);;
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*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, 3)( 2,23)( 4,35)( 5,29)( 6,15)( 7,10)( 8,21)( 9,22)(11,18)
(13,17)(14,19)(16,30)(20,38)(24,41)(25,40)(26,39)(27,42)(32,44)(33,43)(45,47);
s2 := Sym(48)!( 1, 8)( 2, 4)( 3,33)( 5,24)( 6,25)( 7,21)( 9,16)(10,17)(11,32)
(12,29)(13,31)(14,34)(15,43)(18,27)(19,26)(20,46)(22,39)(23,40)(28,35)(30,44)
(36,38)(37,47)(41,42)(45,48);
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, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 
References : None.
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