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Polytope of Type {6,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20}*960d
if this polytope has a name.
Group : SmallGroup(960,10889)
Rank : 3
Schlafli Type : {6,20}
Number of vertices, edges, etc : 24, 240, 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 :
   {6,20,2} of size 1920
Vertex Figure Of :
   {2,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,20}*480, {6,10}*480c
   4-fold quotients : {3,10}*240, {6,5}*240b, {6,10}*240c, {6,10}*240d, {6,10}*240e, {6,10}*240f
   8-fold quotients : {3,5}*120, {3,10}*120a, {3,10}*120b, {6,5}*120b, {6,5}*120c
   16-fold quotients : {3,5}*60
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,20}*1920d, {12,20}*1920l, {12,20}*1920m
Permutation Representation (GAP) :
s0 := ( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)
(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);;
s1 := ( 1, 2)( 3,31)( 4,25)( 5,27)( 6,10)( 8,17)( 9,19)(11,12)(13,43)(14,32)
(15,28)(16,24)(18,26)(20,38)(21,40)(22,42)(29,44)(30,34)(33,35)(45,47)
(49,50);;
s2 := ( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)(11,21)
(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)(35,39)
(36,47)(38,48)(45,46);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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(50)!( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)
(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);
s1 := Sym(50)!( 1, 2)( 3,31)( 4,25)( 5,27)( 6,10)( 8,17)( 9,19)(11,12)(13,43)
(14,32)(15,28)(16,24)(18,26)(20,38)(21,40)(22,42)(29,44)(30,34)(33,35)(45,47)
(49,50);
s2 := Sym(50)!( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)
(11,21)(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)
(35,39)(36,47)(38,48)(45,46);
poly := sub<Sym(50)|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*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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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