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Polytope of Type {5,2,2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,2,4,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 6
Schlafli Type : {5,2,2,4,12}
Number of vertices, edges, etc : 5, 5, 2, 4, 24, 12
Order of s0s1s2s3s4s5 : 60
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
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 : {5,2,2,4,6}*960c
   4-fold quotients : {5,2,2,4,3}*480
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (6,7);;
s3 := ( 8,13)( 9,17)(10,20)(11,21)(12,22)(14,28)(15,29)(16,30)(18,34)(19,35)
(23,40)(24,41)(25,39)(26,42)(27,43)(31,52)(32,50)(33,48)(36,49)(37,51)(38,47)
(44,54)(45,55)(46,53);;
s4 := ( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)(25,41)
(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)(46,55)
(49,52);;
s5 := ( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)(21,29)
(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)(40,48)
(45,51)(47,54)(52,53);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(55)!(2,3)(4,5);
s1 := Sym(55)!(1,2)(3,4);
s2 := Sym(55)!(6,7);
s3 := Sym(55)!( 8,13)( 9,17)(10,20)(11,21)(12,22)(14,28)(15,29)(16,30)(18,34)
(19,35)(23,40)(24,41)(25,39)(26,42)(27,43)(31,52)(32,50)(33,48)(36,49)(37,51)
(38,47)(44,54)(45,55)(46,53);
s4 := Sym(55)!( 9,10)(11,12)(13,23)(15,19)(16,18)(17,31)(20,36)(21,39)(22,24)
(25,41)(26,27)(28,44)(29,47)(30,37)(32,35)(33,51)(34,48)(38,50)(42,53)(43,45)
(46,55)(49,52);
s5 := Sym(55)!( 8,16)( 9,12)(10,27)(11,15)(13,30)(14,19)(17,22)(18,26)(20,43)
(21,29)(23,33)(24,50)(25,36)(28,35)(31,46)(32,41)(34,42)(37,55)(38,44)(39,49)
(40,48)(45,51)(47,54)(52,53);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >; 
 

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