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Polytope of Type {2,8,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2,4}*256
if this polytope has a name.
Group : SmallGroup(256,54027)
Rank : 5
Schlafli Type : {2,8,2,4}
Number of vertices, edges, etc : 2, 8, 8, 4, 4
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,2,4,2} of size 512
   {2,8,2,4,3} of size 768
Vertex Figure Of :
   {2,2,8,2,4} of size 512
   {3,2,8,2,4} of size 768
   {5,2,8,2,4} of size 1280
   {7,2,8,2,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,2,4}*128, {2,8,2,2}*128
   4-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,2,8}*512, {2,8,4,4}*512b, {2,16,2,4}*512
   3-fold covers : {6,8,2,4}*768, {2,8,6,4}*768a, {2,8,2,12}*768, {2,24,2,4}*768
   5-fold covers : {10,8,2,4}*1280, {2,8,10,4}*1280, {2,8,2,20}*1280, {2,40,2,4}*1280
   7-fold covers : {14,8,2,4}*1792, {2,8,14,4}*1792, {2,8,2,28}*1792, {2,56,2,4}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (12,13);;
s4 := (11,12)(13,14);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!(4,5)(6,7)(8,9);
s2 := Sym(14)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(14)!(12,13);
s4 := Sym(14)!(11,12)(13,14);
poly := sub<Sym(14)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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