Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,5,2}

Atlas Canonical Name {10,5,2}*200

Overview

Group
SmallGroup(200,49)
Rank
4
Schläfli Type
{10,5,2}
Vertices, edges, …
10, 25, 5, 2
Order of s0s1s2s3
10
Order of s0s1s2s3s2s1
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

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

Representations

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