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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,10}*400
if this polytope has a name.
Group : SmallGroup(400,218)
Rank : 5
Schlafli Type : {2,2,5,10}
Number of vertices, edges, etc : 2, 2, 5, 25, 10
Order of s0s1s2s3s4 : 10
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,5,10,2} of size 800
   {2,2,5,10,4} of size 1600
   {2,2,5,10,5} of size 2000
Vertex Figure Of :
   {2,2,2,5,10} of size 800
   {3,2,2,5,10} of size 1200
   {4,2,2,5,10} of size 1600
   {5,2,2,5,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,5,10}*800, {2,2,10,10}*800c
   3-fold covers : {6,2,5,10}*1200, {2,2,15,10}*1200
   4-fold covers : {8,2,5,10}*1600, {2,2,20,10}*1600b, {2,4,10,10}*1600b, {4,2,10,10}*1600c, {2,2,10,20}*1600c
   5-fold covers : {2,2,25,10}*2000, {2,2,5,10}*2000, {2,10,5,10}*2000, {10,2,5,10}*2000
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,22)(20,25)(21,24)
(26,29)(27,28);;
s3 := ( 5,11)( 6, 8)( 7,18)( 9,20)(10,14)(12,16)(13,22)(15,26)(17,21)(19,24)
(23,28)(25,27);;
s4 := ( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(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*s1*s0*s1, 
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(29)!(1,2);
s1 := Sym(29)!(3,4);
s2 := Sym(29)!( 6, 7)( 8, 9)(10,13)(11,15)(12,14)(16,17)(18,23)(19,22)(20,25)
(21,24)(26,29)(27,28);
s3 := Sym(29)!( 5,11)( 6, 8)( 7,18)( 9,20)(10,14)(12,16)(13,22)(15,26)(17,21)
(19,24)(23,28)(25,27);
s4 := Sym(29)!( 8, 9)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)
(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*s1*s0*s1, 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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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