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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,2}*256
if this polytope has a name.
Group : SmallGroup(256,53380)
Rank : 5
Schlafli Type : {4,4,2,2}
Number of vertices, edges, etc : 8, 16, 8, 2, 2
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,2,2} of size 512
   {4,4,2,2,3} of size 768
   {4,4,2,2,5} of size 1280
   {4,4,2,2,7} of size 1792
Vertex Figure Of :
   {2,4,4,2,2} of size 512
   {3,4,4,2,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,2,2}*128
   4-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,2,2}*512a, {8,4,2,2}*512a, {4,4,4,2}*512b, {4,4,2,2}*512, {4,8,2,2}*512b, {8,4,2,2}*512b
   3-fold covers : {4,4,2,6}*768, {4,4,6,2}*768a, {4,12,2,2}*768a, {12,4,2,2}*768a
   5-fold covers : {4,4,2,10}*1280, {4,4,10,2}*1280, {4,20,2,2}*1280, {20,4,2,2}*1280
   7-fold covers : {4,4,2,14}*1792, {4,4,14,2}*1792, {4,28,2,2}*1792, {28,4,2,2}*1792
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 6)( 7,10)( 9,12)(11,14)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);;
s2 := ( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);;
s3 := (17,18);;
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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!( 2, 3)( 4, 6)( 7,10)( 9,12)(11,14)(13,15);
s1 := Sym(20)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,11)(10,13)(12,15)(14,16);
s2 := Sym(20)!( 2, 4)( 3, 6)( 5, 8)( 9,12)(11,15)(13,14);
s3 := Sym(20)!(17,18);
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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