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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,2,5}*480
if this polytope has a name.
Group : SmallGroup(480,1087)
Rank : 5
Schlafli Type : {2,12,2,5}
Number of vertices, edges, etc : 2, 12, 12, 5, 5
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,2,5,2} of size 960
Vertex Figure Of :
   {2,2,12,2,5} of size 960
   {3,2,12,2,5} of size 1440
   {4,2,12,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2,5}*240
   3-fold quotients : {2,4,2,5}*160
   4-fold quotients : {2,3,2,5}*120
   6-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2,5}*960a, {2,24,2,5}*960, {2,12,2,10}*960
   3-fold covers : {2,36,2,5}*1440, {6,12,2,5}*1440a, {6,12,2,5}*1440b, {2,12,2,15}*1440
   4-fold covers : {8,12,2,5}*1920a, {4,24,2,5}*1920a, {8,12,2,5}*1920b, {4,24,2,5}*1920b, {4,12,2,5}*1920a, {2,48,2,5}*1920, {2,12,4,10}*1920, {4,12,2,10}*1920a, {2,12,2,20}*1920, {2,24,2,10}*1920, {4,12,2,5}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);;
s2 := ( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);;
s3 := (16,17)(18,19);;
s4 := (15,16)(17,18);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
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*s3*s4*s3*s4*s3*s4, 
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(19)!(1,2);
s1 := Sym(19)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);
s2 := Sym(19)!( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);
s3 := Sym(19)!(16,17)(18,19);
s4 := Sym(19)!(15,16)(17,18);
poly := sub<Sym(19)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, 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*s3*s4*s3*s4*s3*s4, 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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