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Polytope of Type {10,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,10}*400
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 4
Schlafli Type : {10,2,10}
Number of vertices, edges, etc : 10, 10, 10, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,10,2} of size 800
   {10,2,10,4} of size 1600
   {10,2,10,5} of size 2000
Vertex Figure Of :
   {2,10,2,10} of size 800
   {4,10,2,10} of size 1600
   {5,10,2,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,10}*200, {10,2,5}*200
   4-fold quotients : {5,2,5}*100
   5-fold quotients : {2,2,10}*80, {10,2,2}*80
   10-fold quotients : {2,2,5}*40, {5,2,2}*40
   25-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,2,20}*800, {20,2,10}*800, {10,4,10}*800
   3-fold covers : {10,6,10}*1200, {10,2,30}*1200, {30,2,10}*1200
   4-fold covers : {20,2,20}*1600, {10,4,20}*1600, {20,4,10}*1600, {10,2,40}*1600, {40,2,10}*1600, {10,8,10}*1600
   5-fold covers : {10,2,50}*2000, {50,2,10}*2000, {10,10,10}*2000a, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000g
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (13,14)(15,16)(17,18)(19,20);;
s3 := (11,15)(12,13)(14,19)(16,17)(18,20);;
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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(20)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(20)!(13,14)(15,16)(17,18)(19,20);
s3 := Sym(20)!(11,15)(12,13)(14,19)(16,17)(18,20);
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*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 >; 
 

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