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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,5,2}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 5
Schlafli Type : {2,3,5,2}
Number of vertices, edges, etc : 2, 6, 15, 10, 2
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,5,2,2} of size 480
   {2,3,5,2,3} of size 720
   {2,3,5,2,4} of size 960
   {2,3,5,2,5} of size 1200
   {2,3,5,2,6} of size 1440
   {2,3,5,2,7} of size 1680
   {2,3,5,2,8} of size 1920
Vertex Figure Of :
   {2,2,3,5,2} of size 480
   {3,2,3,5,2} of size 720
   {4,2,3,5,2} of size 960
   {5,2,3,5,2} of size 1200
   {6,2,3,5,2} of size 1440
   {7,2,3,5,2} of size 1680
   {8,2,3,5,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,5,2}*480, {2,3,10,2}*480a, {2,3,10,2}*480b, {2,6,5,2}*480b, {2,6,5,2}*480c
   4-fold covers : {2,3,10,4}*960, {4,6,5,2}*960b, {2,3,10,2}*960, {2,6,5,2}*960b, {2,6,10,2}*960c, {2,6,10,2}*960d, {2,6,10,2}*960e, {2,6,10,2}*960f
   6-fold covers : {2,3,10,2}*1440, {2,3,10,6}*1440, {2,3,15,2}*1440, {2,6,15,2}*1440, {6,6,5,2}*1440b
   8-fold covers : {2,3,10,8}*1920, {8,6,5,2}*1920b, {2,3,10,4}*1920, {2,6,10,4}*1920b, {2,6,10,4}*1920c, {2,6,20,2}*1920b, {2,6,20,2}*1920c, {2,12,10,2}*1920c, {2,12,10,2}*1920d, {4,6,5,2}*1920b, {4,6,10,2}*1920d, {4,6,10,2}*1920e, {2,6,10,2}*1920b, {2,3,20,2}*1920, {2,12,5,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(6,7);;
s3 := (4,6)(5,7);;
s4 := (8,9);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(1,2);
s1 := Sym(9)!(4,5)(6,7);
s2 := Sym(9)!(3,4)(6,7);
s3 := Sym(9)!(4,6)(5,7);
s4 := Sym(9)!(8,9);
poly := sub<Sym(9)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s1*s2*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s3 >; 
 

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