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Polytope of Type {2,5,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,20}*960
if this polytope has a name.
Group : SmallGroup(960,10889)
Rank : 4
Schlafli Type : {2,5,20}
Number of vertices, edges, etc : 2, 12, 120, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,20,2} of size 1920
Vertex Figure Of :
   {2,2,5,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,10}*480
   4-fold quotients : {2,5,5}*240, {2,5,10}*240a, {2,5,10}*240b
   8-fold quotients : {2,5,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,20}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4,12)( 5,14)( 6,19)( 7,21)( 9,40)(13,30)(15,46)(16,45)(17,36)(22,25)
(23,38)(24,39)(26,28)(31,35)(32,33)(34,37)(41,49)(42,48)(43,47)(44,50);;
s2 := ( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)
(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49);;
s3 := ( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)(14,31)
(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)(38,40)
(39,49)(43,44)(47,50);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4,12)( 5,14)( 6,19)( 7,21)( 9,40)(13,30)(15,46)(16,45)(17,36)
(22,25)(23,38)(24,39)(26,28)(31,35)(32,33)(34,37)(41,49)(42,48)(43,47)(44,50);
s2 := Sym(50)!( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)
(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49);
s3 := Sym(50)!( 3,10)( 4, 6)( 5,35)( 7,26)( 8,27)( 9,23)(11,18)(12,19)(13,34)
(14,31)(15,33)(16,36)(17,45)(20,29)(21,28)(22,48)(24,41)(25,42)(30,37)(32,46)
(38,40)(39,49)(43,44)(47,50);
poly := sub<Sym(50)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2 >; 
 

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