Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5,10,2,3}

Atlas Canonical Name {2,5,10,2,3}*1200

Overview

Group
SmallGroup(1200,1006)
Rank
6
Schläfli Type
{2,5,10,2,3}
Vertices, edges, …
2, 5, 25, 10, 3, 3
Order of s0s1s2s3s4s5
30
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)(19,22)(24,27)(25,26);;
s2 := ( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)(17,22)(21,26)(23,25);;
s3 := ( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s4 := (29,30);;
s5 := (28,29);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5*s4*s5, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(30)!(1,2);
s1 := Sym(30)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)(19,22)(24,27)(25,26);
s2 := Sym(30)!( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)(17,22)(21,26)(23,25);
s3 := Sym(30)!( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s4 := Sym(30)!(29,30);
s5 := Sym(30)!(28,29);
poly := sub<Sym(30)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;