Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,240408)
Rank
5
Schläfli Type
{2,20,6,4}
Vertices, edges, …
2, 20, 60, 12, 4
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)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56)(49,57)(50,58);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,27)( 8,29)( 9,28)(10,30)(11,23)(12,25)(13,24)(14,26)(15,31)(16,33)(17,32)(18,34)(35,67)(36,69)(37,68)(38,70)(39,75)(40,77)(41,76)(42,78)(43,71)(44,73)(45,72)(46,74)(47,79)(48,81)(49,80)(50,82)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65);;
s3 := ( 5, 6)( 7,15)( 8,16)( 9,18)(10,17)(13,14)(21,22)(23,31)(24,32)(25,34)(26,33)(29,30)(37,38)(39,47)(40,48)(41,50)(42,49)(45,46)(53,54)(55,63)(56,64)(57,66)(58,65)(61,62)(69,70)(71,79)(72,80)(73,82)(74,81)(77,78);;
s4 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 ];;
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)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,65)(42,66)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56)(49,57)(50,58);
s2 := Sym(82)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,27)( 8,29)( 9,28)(10,30)(11,23)(12,25)(13,24)(14,26)(15,31)(16,33)(17,32)(18,34)(35,67)(36,69)(37,68)(38,70)(39,75)(40,77)(41,76)(42,78)(43,71)(44,73)(45,72)(46,74)(47,79)(48,81)(49,80)(50,82)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65);
s3 := Sym(82)!( 5, 6)( 7,15)( 8,16)( 9,18)(10,17)(13,14)(21,22)(23,31)(24,32)(25,34)(26,33)(29,30)(37,38)(39,47)(40,48)(41,50)(42,49)(45,46)(53,54)(55,63)(56,64)(57,66)(58,65)(61,62)(69,70)(71,79)(72,80)(73,82)(74,81)(77,78);
s4 := Sym(82)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)(44,45)(47,50)(48,49)(51,54)(52,53)(55,58)(56,57)(59,62)(60,61)(63,66)(64,65)(67,70)(68,69)(71,74)(72,73)(75,78)(76,77)(79,82)(80,81);
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s3*s2*s4*s3*s4*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s1 >;