Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,8,2}

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

Overview

Group
SmallGroup(1920,240973)
Rank
4
Schläfli Type
{10,8,2}
Vertices, edges, …
60, 240, 48, 2
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 := ( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);;
s1 := ( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)(17,29)(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39);;
s2 := ( 3,23)( 4,24)( 5,26)( 6,25)( 7,36)( 8,35)( 9,38)(10,37)(11,12)(15,21)(16,22)(17,20)(18,19)(27,28)(33,34)(39,42)(40,41);;
s3 := (43,44);;
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*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(44)!( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);
s1 := Sym(44)!( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)(17,29)(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39);
s2 := Sym(44)!( 3,23)( 4,24)( 5,26)( 6,25)( 7,36)( 8,35)( 9,38)(10,37)(11,12)(15,21)(16,22)(17,20)(18,19)(27,28)(33,34)(39,42)(40,41);
s3 := Sym(44)!(43,44);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;