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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,8,2}*256a
if this polytope has a name.
Group : SmallGroup(256,53335)
Rank : 5
Schlafli Type : {2,4,8,2}
Number of vertices, edges, etc : 2, 4, 16, 8, 2
Order of s₀s₁s₂s₃s₄ : 8
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,8,2,2} of size 512
   {2,4,8,2,3} of size 768
   {2,4,8,2,5} of size 1280
   {2,4,8,2,7} of size 1792
Vertex Figure Of :
   {2,2,4,8,2} of size 512
   {3,2,4,8,2} of size 768
   {5,2,4,8,2} of size 1280
   {7,2,4,8,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,4,2}*128, {2,2,8,2}*128
   4-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,8,2}*512a, {2,8,8,2}*512a, {2,8,8,2}*512b, {2,4,8,4}*512a, {4,4,8,2}*512b, {2,4,16,2}*512a, {2,4,16,2}*512b
   3-fold covers : {2,4,8,6}*768a, {6,4,8,2}*768a, {2,12,8,2}*768a, {2,4,24,2}*768a
   5-fold covers : {2,4,8,10}*1280a, {10,4,8,2}*1280a, {2,20,8,2}*1280a, {2,4,40,2}*1280a
   7-fold covers : {2,4,8,14}*1792a, {14,4,8,2}*1792a, {2,28,8,2}*1792a, {2,4,56,2}*1792a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 6)( 5, 8)(12,15)(14,17);;
s2 := ( 3, 4)( 5, 7)( 6, 9)( 8,11)(10,12)(13,15)(14,16)(17,18);;
s3 := ( 4, 5)( 6, 8)( 7,10)(11,13)(12,14)(15,17);;
s4 := (19,20);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 4, 6)( 5, 8)(12,15)(14,17);
s2 := Sym(20)!( 3, 4)( 5, 7)( 6, 9)( 8,11)(10,12)(13,15)(14,16)(17,18);
s3 := Sym(20)!( 4, 5)( 6, 8)( 7,10)(11,13)(12,14)(15,17);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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