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Polytope of Type {3,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,5,2}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 4
Schlafli Type : {3,5,2}
Number of vertices, edges, etc : 12, 30, 20, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,5,2,2} of size 480
   {3,5,2,3} of size 720
   {3,5,2,4} of size 960
   {3,5,2,5} of size 1200
   {3,5,2,6} of size 1440
   {3,5,2,7} of size 1680
   {3,5,2,8} of size 1920
Vertex Figure Of :
   {2,3,5,2} of size 480
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,5,2}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,10,2}*480, {6,5,2}*480b
   3-fold covers : {3,15,2}*720
   4-fold covers : {3,10,4}*960, {3,20,2}*960, {12,5,2}*960, {6,10,2}*960c
   5-fold covers : {15,5,2}*1200
   6-fold covers : {3,10,6}*1440, {3,10,2}*1440b, {3,30,2}*1440, {6,15,2}*1440c, {6,15,2}*1440d
   8-fold covers : {3,10,8}*1920, {6,10,4}*1920c, {6,20,2}*1920c, {12,10,2}*1920c, {3,20,4}*1920, {6,20,2}*1920e, {12,10,2}*1920e, {6,10,2}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);;
s1 := ( 1, 2)( 3, 4)( 5,11)( 8,10);;
s2 := ( 1, 3)( 2, 6)( 8, 9)(10,11);;
s3 := (13,14);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!( 2, 9)( 4,12)( 5, 7)( 6, 8);
s1 := Sym(14)!( 1, 2)( 3, 4)( 5,11)( 8,10);
s2 := Sym(14)!( 1, 3)( 2, 6)( 8, 9)(10,11);
s3 := Sym(14)!(13,14);
poly := sub<Sym(14)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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