Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,10,12}

Atlas Canonical Name {2,10,12}*1920e

Overview

Group
SmallGroup(1920,240988)
Rank
4
Schläfli Type
{2,10,12}
Vertices, edges, …
2, 40, 240, 48
Order of s0s1s2s3
20
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 := ( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)(14,36)(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44);;
s2 := ( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49)(51,52);;
s3 := ( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)(12,38)(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)(26,50)(28,39)(29,47)(41,44);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*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*s2*s3*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!(1,2);
s1 := Sym(52)!( 4,47)( 5,43)( 6,19)( 7,21)( 9,32)(10,50)(11,38)(12,49)(13,25)(14,36)(15,24)(16,42)(17,41)(22,28)(23,31)(26,40)(27,39)(29,48)(30,33)(37,44);
s2 := Sym(52)!( 4, 5)( 6,19)( 7,21)( 9,30)(10,37)(11,31)(12,17)(13,28)(14,41)(15,27)(16,29)(22,40)(23,35)(24,46)(25,33)(26,32)(34,44)(36,43)(42,45)(47,49)(51,52);
s3 := Sym(52)!( 3,34)( 4,48)( 5,15)( 6,14)( 7,33)( 8,46)( 9,42)(10,40)(11,49)(12,38)(13,31)(16,32)(17,37)(18,35)(19,36)(20,45)(21,30)(22,27)(23,25)(24,43)(26,50)(28,39)(29,47)(41,44);
poly := sub<Sym(52)|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, s3*s1*s2*s3*s2*s3*s2*s3*s1*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*s2*s3*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s1*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2 >;