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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2,2,5}*1920a
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 6
Schlafli Type : {4,12,2,2,5}
Number of vertices, edges, etc : 4, 24, 12, 2, 5, 5
Order of s0s1s2s3s4s5 : 60
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,12,2,2,5}*960, {4,6,2,2,5}*960a
   3-fold quotients : {4,4,2,2,5}*640
   4-fold quotients : {2,6,2,2,5}*480
   6-fold quotients : {2,4,2,2,5}*320, {4,2,2,2,5}*320
   8-fold quotients : {2,3,2,2,5}*240
   12-fold quotients : {2,2,2,2,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s1 := ( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)(16,23)
(19,22)(20,21);;
s2 := ( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)(16,20);;
s3 := (25,26);;
s4 := (28,29)(30,31);;
s5 := (27,28)(29,30);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(31)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s1 := Sym(31)!( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)
(16,23)(19,22)(20,21);
s2 := Sym(31)!( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)
(16,20);
s3 := Sym(31)!(25,26);
s4 := Sym(31)!(28,29)(30,31);
s5 := Sym(31)!(27,28)(29,30);
poly := sub<Sym(31)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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