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Polytope of Type {2,2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,16}*128
if this polytope has a name.
Group : SmallGroup(128,2140)
Rank : 4
Schlafli Type : {2,2,16}
Number of vertices, edges, etc : 2, 2, 16, 16
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,16,2} of size 256
   {2,2,16,4} of size 512
   {2,2,16,4} of size 512
   {2,2,16,6} of size 768
   {2,2,16,10} of size 1280
   {2,2,16,14} of size 1792
Vertex Figure Of :
   {2,2,2,16} of size 256
   {3,2,2,16} of size 384
   {4,2,2,16} of size 512
   {5,2,2,16} of size 640
   {6,2,2,16} of size 768
   {7,2,2,16} of size 896
   {9,2,2,16} of size 1152
   {10,2,2,16} of size 1280
   {11,2,2,16} of size 1408
   {13,2,2,16} of size 1664
   {14,2,2,16} of size 1792
   {15,2,2,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,8}*64
   4-fold quotients : {2,2,4}*32
   8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,16}*256a, {4,2,16}*256, {2,2,32}*256
   3-fold covers : {2,2,48}*384, {2,6,16}*384, {6,2,16}*384
   4-fold covers : {2,4,16}*512a, {2,8,16}*512c, {2,8,16}*512d, {4,4,16}*512a, {2,4,32}*512a, {2,4,32}*512b, {2,2,64}*512
   5-fold covers : {2,2,80}*640, {2,10,16}*640, {10,2,16}*640
   6-fold covers : {6,4,16}*768a, {2,12,16}*768a, {2,4,48}*768a, {4,6,16}*768a, {12,2,16}*768, {4,2,48}*768, {2,6,32}*768, {6,2,32}*768, {2,2,96}*768
   7-fold covers : {2,2,112}*896, {2,14,16}*896, {14,2,16}*896
   9-fold covers : {2,18,16}*1152, {18,2,16}*1152, {2,2,144}*1152, {6,6,16}*1152a, {6,6,16}*1152b, {6,6,16}*1152c, {2,6,48}*1152a, {2,6,48}*1152b, {2,6,48}*1152c, {6,2,48}*1152, {2,6,16}*1152
   10-fold covers : {10,4,16}*1280a, {2,20,16}*1280a, {2,4,80}*1280a, {4,10,16}*1280, {20,2,16}*1280, {4,2,80}*1280, {2,10,32}*1280, {10,2,32}*1280, {2,2,160}*1280
   11-fold covers : {2,22,16}*1408, {22,2,16}*1408, {2,2,176}*1408
   13-fold covers : {2,26,16}*1664, {26,2,16}*1664, {2,2,208}*1664
   14-fold covers : {14,4,16}*1792a, {2,28,16}*1792a, {2,4,112}*1792a, {4,14,16}*1792, {28,2,16}*1792, {4,2,112}*1792, {2,14,32}*1792, {14,2,32}*1792, {2,2,224}*1792
   15-fold covers : {2,30,16}*1920, {30,2,16}*1920, {2,2,240}*1920, {6,10,16}*1920, {10,6,16}*1920, {2,10,48}*1920, {10,2,48}*1920, {2,6,80}*1920, {6,2,80}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!(3,4);
s2 := Sym(20)!( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s3 := Sym(20)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
poly := sub<Sym(20)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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