Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,235343)
Rank
5
Schläfli Type
{8,2,6,10}
Vertices, edges, …
8, 8, 6, 30, 10
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

10-fold

12-fold

15-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 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(15,16)(19,21)(20,22)(25,27)(26,28)(31,33)(32,34)(35,37)(36,38);;
s3 := ( 9,11)(10,15)(13,20)(14,19)(17,26)(18,25)(21,22)(23,32)(24,31)(27,28)(29,36)(30,35)(33,34)(37,38);;
s4 := ( 9,17)(10,13)(11,25)(12,27)(14,29)(15,19)(16,21)(18,23)(20,35)(22,37)(24,30)(26,31)(28,33)(32,36)(34,38);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*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*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(38)!(2,3)(4,5)(6,7);
s1 := Sym(38)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(38)!(11,12)(15,16)(19,21)(20,22)(25,27)(26,28)(31,33)(32,34)(35,37)(36,38);
s3 := Sym(38)!( 9,11)(10,15)(13,20)(14,19)(17,26)(18,25)(21,22)(23,32)(24,31)(27,28)(29,36)(30,35)(33,34)(37,38);
s4 := Sym(38)!( 9,17)(10,13)(11,25)(12,27)(14,29)(15,19)(16,21)(18,23)(20,35)(22,37)(24,30)(26,31)(28,33)(32,36)(34,38);
poly := sub<Sym(38)|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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*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*s3*s4*s3*s4 >;