Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,30,6}

Atlas Canonical Name {2,2,30,6}*1440b

Overview

Group
SmallGroup(1440,5949)
Rank
5
Schläfli Type
{2,2,30,6}
Vertices, edges, …
2, 2, 30, 90, 6
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(21,24)(22,23)(25,30)(26,34)(27,33)(28,32)(29,31)(36,39)(37,38)(40,45)(41,49)(42,48)(43,47)(44,46)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(66,69)(67,68)(70,75)(71,79)(72,78)(73,77)(74,76)(81,84)(82,83)(85,90)(86,94)(87,93)(88,92)(89,91);;
s3 := ( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(30,46)(31,45)(32,49)(33,48)(34,47)(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64)(65,86)(66,85)(67,89)(68,88)(69,87)(70,81)(71,80)(72,84)(73,83)(74,82)(75,91)(76,90)(77,94)(78,93)(79,92);;
s4 := ( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(32,62)(33,63)(34,64)(35,80)(36,81)(37,82)(38,83)(39,84)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(94)!(1,2);
s1 := Sym(94)!(3,4);
s2 := Sym(94)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(21,24)(22,23)(25,30)(26,34)(27,33)(28,32)(29,31)(36,39)(37,38)(40,45)(41,49)(42,48)(43,47)(44,46)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(66,69)(67,68)(70,75)(71,79)(72,78)(73,77)(74,76)(81,84)(82,83)(85,90)(86,94)(87,93)(88,92)(89,91);
s3 := Sym(94)!( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,41)(21,40)(22,44)(23,43)(24,42)(25,36)(26,35)(27,39)(28,38)(29,37)(30,46)(31,45)(32,49)(33,48)(34,47)(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64)(65,86)(66,85)(67,89)(68,88)(69,87)(70,81)(71,80)(72,84)(73,83)(74,82)(75,91)(76,90)(77,94)(78,93)(79,92);
s4 := Sym(94)!( 5,65)( 6,66)( 7,67)( 8,68)( 9,69)(10,70)(11,71)(12,72)(13,73)(14,74)(15,75)(16,76)(17,77)(18,78)(19,79)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(32,62)(33,63)(34,64)(35,80)(36,81)(37,82)(38,83)(39,84)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94);
poly := sub<Sym(94)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;