Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,4,6,20}

Atlas Canonical Name {2,4,6,20}*1920c

Overview

Group
SmallGroup(1920,240408)
Rank
5
Schläfli Type
{2,4,6,20}
Vertices, edges, …
2, 4, 12, 60, 20
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

5-fold

10-fold

Covers minimal covers in bold

None in this atlas.

Representations

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