Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,10,4}

Atlas Canonical Name {3,2,4,10,4}*1920

Overview

Group
SmallGroup(1920,208118)
Rank
6
Schläfli Type
{3,2,4,10,4}
Vertices, edges, …
3, 3, 4, 20, 20, 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 := (44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);;
s3 := ( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,74)(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)(35,68)(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);;
s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,40)(25,39)(26,43)(27,42)(28,41)(29,35)(30,34)(31,38)(32,37)(33,36)(44,45)(46,48)(49,50)(51,53)(54,55)(56,58)(59,60)(61,63)(64,80)(65,79)(66,83)(67,82)(68,81)(69,75)(70,74)(71,78)(72,77)(73,76);;
s5 := ( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(44,74)(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,64)(55,65)(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);
s3 := Sym(83)!( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,74)(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)(35,68)(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);
s4 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,40)(25,39)(26,43)(27,42)(28,41)(29,35)(30,34)(31,38)(32,37)(33,36)(44,45)(46,48)(49,50)(51,53)(54,55)(56,58)(59,60)(61,63)(64,80)(65,79)(66,83)(67,82)(68,81)(69,75)(70,74)(71,78)(72,77)(73,76);
s5 := Sym(83)!( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(44,74)(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,64)(55,65)(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73);
poly := sub<Sym(83)|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, 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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, 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 >;