Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,2,10,8}

Atlas Canonical Name {6,2,10,8}*1920

Overview

Group
SmallGroup(1920,235343)
Rank
5
Schläfli Type
{6,2,10,8}
Vertices, edges, …
6, 6, 10, 40, 8
Order of s0s1s2s3s4
120
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

16-fold

20-fold

24-fold

30-fold

40-fold

60-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)(33,36)(34,35)(38,41)(39,40)(43,46)(44,45);;
s3 := ( 7, 8)( 9,11)(12,13)(14,16)(17,23)(18,22)(19,26)(20,25)(21,24)(27,43)(28,42)(29,46)(30,45)(31,44)(32,38)(33,37)(34,41)(35,40)(36,39);;
s4 := ( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,42)(18,43)(19,44)(20,45)(21,46)(22,37)(23,38)(24,39)(25,40)(26,41);;
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, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(46)!(3,4)(5,6);
s1 := Sym(46)!(1,5)(2,3)(4,6);
s2 := Sym(46)!( 8,11)( 9,10)(13,16)(14,15)(18,21)(19,20)(23,26)(24,25)(28,31)(29,30)(33,36)(34,35)(38,41)(39,40)(43,46)(44,45);
s3 := Sym(46)!( 7, 8)( 9,11)(12,13)(14,16)(17,23)(18,22)(19,26)(20,25)(21,24)(27,43)(28,42)(29,46)(30,45)(31,44)(32,38)(33,37)(34,41)(35,40)(36,39);
s4 := Sym(46)!( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,42)(18,43)(19,44)(20,45)(21,46)(22,37)(23,38)(24,39)(25,40)(26,41);
poly := sub<Sym(46)|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, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;