Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,30}

Atlas Canonical Name {2,6,30}*720b

Overview

Group
SmallGroup(720,831)
Rank
4
Schläfli Type
{2,6,30}
Vertices, edges, …
2, 6, 90, 30
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

3-fold

5-fold

6-fold

9-fold

15-fold

18-fold

30-fold

45-fold

Covers minimal covers in bold

2-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92);;
s2 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89);;
s3 := ( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,69)(19,68)(20,72)(21,71)(22,70)(23,64)(24,63)(25,67)(26,66)(27,65)(28,74)(29,73)(30,77)(31,76)(32,75)(33,84)(34,83)(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)(45,92)(46,91)(47,90);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*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*s2*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*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(92)!(1,2);
s1 := Sym(92)!(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(31,46)(32,47)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90)(76,91)(77,92);
s2 := Sym(92)!( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89);
s3 := Sym(92)!( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,69)(19,68)(20,72)(21,71)(22,70)(23,64)(24,63)(25,67)(26,66)(27,65)(28,74)(29,73)(30,77)(31,76)(32,75)(33,84)(34,83)(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)(45,92)(46,91)(47,90);
poly := sub<Sym(92)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*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*s2*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*s2*s3*s2*s3*s2*s3*s2*s3 >;