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Polytope of Type {5,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5,2}*320
if this polytope has a name.
Group : SmallGroup(320,1636)
Rank : 4
Schlafli Type : {5,5,2}
Number of vertices, edges, etc : 16, 40, 16, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,5,2,2} of size 640
   {5,5,2,3} of size 960
   {5,5,2,4} of size 1280
   {5,5,2,5} of size 1600
   {5,5,2,6} of size 1920
Vertex Figure Of :
   {2,5,5,2} of size 640
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,5,2}*640, {5,10,2}*640a, {10,5,2}*640a, {5,10,2}*640b, {10,5,2}*640b
   4-fold covers : {5,10,4}*1280, {5,10,2}*1280, {10,5,2}*1280, {10,10,2}*1280a, {10,10,2}*1280b, {10,10,2}*1280c, {5,20,2}*1280a, {5,20,2}*1280b, {20,5,2}*1280a, {20,5,2}*1280b, {10,10,2}*1280d
   6-fold covers : {5,10,6}*1920, {10,15,2}*1920, {15,10,2}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14);;
s1 := ( 2, 9)( 3,12)( 5,15)( 6, 7)( 8,14)(13,16);;
s2 := ( 1, 2)( 7, 8)( 9,15)(10,16)(11,14)(12,13);;
s3 := (17,18);;
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*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14);
s1 := Sym(18)!( 2, 9)( 3,12)( 5,15)( 6, 7)( 8,14)(13,16);
s2 := Sym(18)!( 1, 2)( 7, 8)( 9,15)(10,16)(11,14)(12,13);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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