Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,10,8}

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

Overview

Group
SmallGroup(1920,240973)
Rank
4
Schläfli Type
{2,10,8}
Vertices, edges, …
2, 60, 240, 48
Order of s0s1s2s3
6
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

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