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Polytope of Type {10,2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,16}*640
if this polytope has a name.
Group : SmallGroup(640,15829)
Rank : 4
Schlafli Type : {10,2,16}
Number of vertices, edges, etc : 10, 10, 16, 16
Order of s0s1s2s3 : 80
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,16,2} of size 1280
Vertex Figure Of :
   {2,10,2,16} of size 1280
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,16}*320, {10,2,8}*320
   4-fold quotients : {5,2,8}*160, {10,2,4}*160
   5-fold quotients : {2,2,16}*128
   8-fold quotients : {5,2,4}*80, {10,2,2}*80
   10-fold quotients : {2,2,8}*64
   16-fold quotients : {5,2,2}*40
   20-fold quotients : {2,2,4}*32
   40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,4,16}*1280a, {20,2,16}*1280, {10,2,32}*1280
   3-fold covers : {30,2,16}*1920, {10,6,16}*1920, {10,2,48}*1920
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s3 := (11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(26)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(26)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(26)!(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);
s3 := Sym(26)!(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
poly := sub<Sym(26)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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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