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Polytope of Type {4,2,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,10,5}*800
if this polytope has a name.
Group : SmallGroup(800,1134)
Rank : 5
Schlafli Type : {4,2,10,5}
Number of vertices, edges, etc : 4, 4, 10, 25, 5
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,10,5,2} of size 1600
Vertex Figure Of :
   {2,4,2,10,5} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,10,5}*400
   5-fold quotients : {4,2,2,5}*160
   10-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,2,10,5}*1600, {4,4,10,5}*1600, {4,2,10,10}*1600b
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29);;
s3 := ( 5, 8)( 6,14)( 7,11)( 9,16)(10,22)(12,24)(13,18)(15,20)(19,28)(21,25)
(23,26)(27,29);;
s4 := ( 5, 6)( 7,10)( 8,12)( 9,11)(14,19)(15,18)(16,21)(17,20)(22,23)(24,27)
(25,26)(28,29);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!(2,3);
s1 := Sym(29)!(1,2)(3,4);
s2 := Sym(29)!( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)
(28,29);
s3 := Sym(29)!( 5, 8)( 6,14)( 7,11)( 9,16)(10,22)(12,24)(13,18)(15,20)(19,28)
(21,25)(23,26)(27,29);
s4 := Sym(29)!( 5, 6)( 7,10)( 8,12)( 9,11)(14,19)(15,18)(16,21)(17,20)(22,23)
(24,27)(25,26)(28,29);
poly := sub<Sym(29)|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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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