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Polytope of Type {2,2,3,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,5,2}*480
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 6
Schlafli Type : {2,2,3,5,2}
Number of vertices, edges, etc : 2, 2, 6, 15, 10, 2
Order of s0s1s2s3s4s5 : 10
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,3,5,2,2} of size 960
   {2,2,3,5,2,3} of size 1440
   {2,2,3,5,2,4} of size 1920
Vertex Figure Of :
   {2,2,2,3,5,2} of size 960
   {3,2,2,3,5,2} of size 1440
   {4,2,2,3,5,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,3,5,2}*960, {2,2,3,5,2}*960, {2,2,3,10,2}*960a, {2,2,3,10,2}*960b, {2,2,6,5,2}*960b, {2,2,6,5,2}*960c
   3-fold covers : {6,2,3,5,2}*1440
   4-fold covers : {8,2,3,5,2}*1920, {2,2,3,10,4}*1920, {2,4,6,5,2}*1920b, {4,2,3,5,2}*1920, {4,2,3,10,2}*1920a, {4,2,3,10,2}*1920b, {4,2,6,5,2}*1920b, {4,2,6,5,2}*1920c, {2,2,3,10,2}*1920, {2,2,6,5,2}*1920b, {2,2,6,10,2}*1920c, {2,2,6,10,2}*1920d, {2,2,6,10,2}*1920e, {2,2,6,10,2}*1920f
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (6,7)(8,9);;
s3 := (5,6)(8,9);;
s4 := (6,8)(7,9);;
s5 := (10,11);;
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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, 
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s2*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!(1,2);
s1 := Sym(11)!(3,4);
s2 := Sym(11)!(6,7)(8,9);
s3 := Sym(11)!(5,6)(8,9);
s4 := Sym(11)!(6,8)(7,9);
s5 := Sym(11)!(10,11);
poly := sub<Sym(11)|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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*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, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s3*s2*s3*s4*s3*s2*s4*s3*s2*s4*s3*s2*s4*s3*s4 >; 
 

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