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Polytope of Type {2,4,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,16}*256b
if this polytope has a name.
Group : SmallGroup(256,26516)
Rank : 4
Schlafli Type : {2,4,16}
Number of vertices, edges, etc : 2, 4, 32, 16
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,16,2} of size 512
Vertex Figure Of :
   {2,2,4,16} of size 512
   {3,2,4,16} of size 768
   {5,2,4,16} of size 1280
   {7,2,4,16} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,8}*128a
   4-fold quotients : {2,4,4}*64, {2,2,8}*64
   8-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,16}*512a, {2,8,16}*512e, {2,8,16}*512f, {4,4,16}*512b
   3-fold covers : {6,4,16}*768b, {2,12,16}*768b, {2,4,48}*768b
   5-fold covers : {10,4,16}*1280b, {2,20,16}*1280b, {2,4,80}*1280b
   7-fold covers : {14,4,16}*1792b, {2,28,16}*1792b, {2,4,112}*1792b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 8)( 9,10)(15,16)(17,18);;
s2 := ( 5, 6)( 7, 9)( 8,10)(11,15)(12,16)(13,18)(14,17);;
s3 := ( 3,11)( 4,12)( 5,14)( 6,13)( 7,17)( 8,18)( 9,15)(10,16);;
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, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 7, 8)( 9,10)(15,16)(17,18);
s2 := Sym(18)!( 5, 6)( 7, 9)( 8,10)(11,15)(12,16)(13,18)(14,17);
s3 := Sym(18)!( 3,11)( 4,12)( 5,14)( 6,13)( 7,17)( 8,18)( 9,15)(10,16);
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, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 

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