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Polytope of Type {2,5,5}

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

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