Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,6,10,6}

Atlas Canonical Name {2,6,10,6}*1440

Overview

Group
SmallGroup(1440,5924)
Rank
5
Schläfli Type
{2,6,10,6}
Vertices, edges, …
2, 6, 30, 30, 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

9-fold

10-fold

15-fold

18-fold

20-fold

30-fold

45-fold

Covers minimal covers in bold

None in this atlas.

Representations

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