Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,10,6}

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

Overview

Group
SmallGroup(1920,240990)
Rank
4
Schläfli Type
{2,10,6}
Vertices, edges, …
2, 80, 240, 48
Order of s0s1s2s3
10
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

16-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4,29)( 5,21)( 6,17)( 9,24)(10,50)(11,30)(12,45)(13,27)(14,49)(15,37)(16,39)(18,34)(20,23)(25,44)(26,28)(31,38)(32,47)(33,35)(42,43)(46,48);;
s2 := ( 4,12)( 5,13)( 9,39)(10,25)(11,27)(14,28)(15,29)(16,30)(20,37)(21,24)(22,49)(23,35)(26,42)(31,43)(32,44)(33,45)(36,48)(38,40)(41,47)(46,50);;
s3 := ( 3,22)( 4,44)( 5,32)( 6,24)( 7,41)( 8,40)( 9,17)(10,45)(11,43)(12,50)(13,26)(14,33)(15,31)(16,46)(18,20)(19,36)(21,47)(23,34)(25,29)(27,28)(30,42)(35,49)(37,38)(39,48);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*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*s3*s2*s1*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 4,29)( 5,21)( 6,17)( 9,24)(10,50)(11,30)(12,45)(13,27)(14,49)(15,37)(16,39)(18,34)(20,23)(25,44)(26,28)(31,38)(32,47)(33,35)(42,43)(46,48);
s2 := Sym(50)!( 4,12)( 5,13)( 9,39)(10,25)(11,27)(14,28)(15,29)(16,30)(20,37)(21,24)(22,49)(23,35)(26,42)(31,43)(32,44)(33,45)(36,48)(38,40)(41,47)(46,50);
s3 := Sym(50)!( 3,22)( 4,44)( 5,32)( 6,24)( 7,41)( 8,40)( 9,17)(10,45)(11,43)(12,50)(13,26)(14,33)(15,31)(16,46)(18,20)(19,36)(21,47)(23,34)(25,29)(27,28)(30,42)(35,49)(37,38)(39,48);
poly := sub<Sym(50)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s3*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*s3*s2*s1*s2*s3*s2*s3 >;