Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,5,8,2}

Atlas Canonical Name {2,5,8,2}*1920

Overview

Group
SmallGroup(1920,240973)
Rank
5
Schläfli Type
{2,5,8,2}
Vertices, edges, …
2, 30, 120, 48, 2
Order of s0s1s2s3s4
6
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

4-fold

Covers minimal covers in bold

None in this atlas.

Representations

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