Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,2,20,4}

Atlas Canonical Name {3,2,2,20,4}*1920

Overview

Group
SmallGroup(1920,205034)
Rank
6
Schläfli Type
{3,2,2,20,4}
Vertices, edges, …
3, 3, 2, 20, 40, 4
Order of s0s1s2s3s4s5
60
Order of s0s1s2s3s4s5s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

5-fold

8-fold

10-fold

20-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,36)(27,40)(28,39)(29,38)(30,37)(31,41)(32,45)(33,44)(34,43)(35,42)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(66,76)(67,80)(68,79)(69,78)(70,77)(71,81)(72,85)(73,84)(74,83)(75,82);;
s4 := ( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,32)(12,31)(13,35)(14,34)(15,33)(16,37)(17,36)(18,40)(19,39)(20,38)(21,42)(22,41)(23,45)(24,44)(25,43)(46,67)(47,66)(48,70)(49,69)(50,68)(51,72)(52,71)(53,75)(54,74)(55,73)(56,77)(57,76)(58,80)(59,79)(60,78)(61,82)(62,81)(63,85)(64,84)(65,83);;
s5 := ( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,71)(27,72)(28,73)(29,74)(30,75)(31,66)(32,67)(33,68)(34,69)(35,70)(36,81)(37,82)(38,83)(39,84)(40,85)(41,76)(42,77)(43,78)(44,79)(45,80);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(85)!(2,3);
s1 := Sym(85)!(1,2);
s2 := Sym(85)!(4,5);
s3 := Sym(85)!( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(26,36)(27,40)(28,39)(29,38)(30,37)(31,41)(32,45)(33,44)(34,43)(35,42)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(62,65)(63,64)(66,76)(67,80)(68,79)(69,78)(70,77)(71,81)(72,85)(73,84)(74,83)(75,82);
s4 := Sym(85)!( 6,27)( 7,26)( 8,30)( 9,29)(10,28)(11,32)(12,31)(13,35)(14,34)(15,33)(16,37)(17,36)(18,40)(19,39)(20,38)(21,42)(22,41)(23,45)(24,44)(25,43)(46,67)(47,66)(48,70)(49,69)(50,68)(51,72)(52,71)(53,75)(54,74)(55,73)(56,77)(57,76)(58,80)(59,79)(60,78)(61,82)(62,81)(63,85)(64,84)(65,83);
s5 := Sym(85)!( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,71)(27,72)(28,73)(29,74)(30,75)(31,66)(32,67)(33,68)(34,69)(35,70)(36,81)(37,82)(38,83)(39,84)(40,85)(41,76)(42,77)(43,78)(44,79)(45,80);
poly := sub<Sym(85)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;