Part of the Atlas of Small Regular Polytopes

Polytope of Type {40,2,12}

Atlas Canonical Name {40,2,12}*1920

Overview

Group
SmallGroup(1920,182161)
Rank
4
Schläfli Type
{40,2,12}
Vertices, edges, …
40, 40, 12, 12
Order of s0s1s2s3
120
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

3-fold

4-fold

5-fold

6-fold

8-fold

10-fold

12-fold

15-fold

16-fold

20-fold

24-fold

30-fold

32-fold

40-fold

48-fold

60-fold

80-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);;
s1 := ( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);;
s2 := (42,43)(44,45)(47,50)(48,49)(51,52);;
s3 := (41,47)(42,44)(43,51)(45,48)(46,49)(50,52);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(52)!( 2, 3)( 4, 5)( 6, 9)( 7,11)( 8,10)(12,13)(14,19)(15,21)(16,20)(17,23)(18,22)(25,30)(26,29)(27,32)(28,31)(33,34)(35,38)(36,37)(39,40);
s1 := Sym(52)!( 1, 7)( 2, 4)( 3,15)( 5,17)( 6,10)( 8,12)( 9,25)(11,27)(13,18)(14,20)(16,22)(19,33)(21,35)(23,28)(24,29)(26,31)(30,39)(32,36)(34,37)(38,40);
s2 := Sym(52)!(42,43)(44,45)(47,50)(48,49)(51,52);
s3 := Sym(52)!(41,47)(42,44)(43,51)(45,48)(46,49)(50,52);
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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;