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Polytope of Type {4,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,2}*256a
if this polytope has a name.
Group : SmallGroup(256,11082)
Rank : 4
Schlafli Type : {4,8,2}
Number of vertices, edges, etc : 8, 32, 16, 2
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,8,2,2} of size 512
   {4,8,2,3} of size 768
   {4,8,2,5} of size 1280
   {4,8,2,7} of size 1792
Vertex Figure Of :
   {2,4,8,2} of size 512
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,8,2}*128a, {4,8,2}*128b, {4,4,2}*128
   4-fold quotients : {4,4,2}*64, {2,8,2}*64
   8-fold quotients : {2,4,2}*32, {4,2,2}*32
   16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,8,2}*512a, {4,8,4}*512a, {4,8,2}*512a, {8,8,2}*512c, {4,16,2}*512a, {4,16,2}*512b
   3-fold covers : {4,8,6}*768a, {12,8,2}*768a, {4,24,2}*768a
   5-fold covers : {4,8,10}*1280a, {20,8,2}*1280a, {4,40,2}*1280a
   7-fold covers : {4,8,14}*1792a, {28,8,2}*1792a, {4,56,2}*1792a
Permutation Representation (GAP) :
s0 := ( 5, 6)( 7, 8)(13,14)(15,16);;
s1 := ( 5, 7)( 6, 8)( 9,13)(10,14)(11,15)(12,16);;
s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);;
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, s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 5, 6)( 7, 8)(13,14)(15,16);
s1 := Sym(18)!( 5, 7)( 6, 8)( 9,13)(10,14)(11,15)(12,16);
s2 := Sym(18)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,15)( 6,16)( 7,13)( 8,14);
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, 
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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