Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,30,12}

Atlas Canonical Name {2,30,12}*1440d

Overview

Group
SmallGroup(1440,5900)
Rank
4
Schläfli Type
{2,30,12}
Vertices, edges, …
2, 30, 180, 12
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

6-fold

15-fold

30-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := ( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(24,25)(27,39)(28,41)(29,40)(30,42)(31,35)(32,37)(33,36)(34,38)(44,45)(47,59)(48,61)(49,60)(50,62)(51,55)(52,57)(53,56)(54,58);;
s2 := ( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,19)(12,22)(13,21)(14,20)(16,18)(23,47)(24,50)(25,49)(26,48)(27,43)(28,46)(29,45)(30,44)(31,59)(32,62)(33,61)(34,60)(35,55)(36,58)(37,57)(38,56)(39,51)(40,54)(41,53)(42,52);;
s3 := ( 3,26)( 4,25)( 5,24)( 6,23)( 7,30)( 8,29)( 9,28)(10,27)(11,34)(12,33)(13,32)(14,31)(15,38)(16,37)(17,36)(18,35)(19,42)(20,41)(21,40)(22,39)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61);;
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*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!(1,2);
s1 := Sym(62)!( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(24,25)(27,39)(28,41)(29,40)(30,42)(31,35)(32,37)(33,36)(34,38)(44,45)(47,59)(48,61)(49,60)(50,62)(51,55)(52,57)(53,56)(54,58);
s2 := Sym(62)!( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,19)(12,22)(13,21)(14,20)(16,18)(23,47)(24,50)(25,49)(26,48)(27,43)(28,46)(29,45)(30,44)(31,59)(32,62)(33,61)(34,60)(35,55)(36,58)(37,57)(38,56)(39,51)(40,54)(41,53)(42,52);
s3 := Sym(62)!( 3,26)( 4,25)( 5,24)( 6,23)( 7,30)( 8,29)( 9,28)(10,27)(11,34)(12,33)(13,32)(14,31)(15,38)(16,37)(17,36)(18,35)(19,42)(20,41)(21,40)(22,39)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61);
poly := sub<Sym(62)|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*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;