Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,40,2,2}

Atlas Canonical Name {4,40,2,2}*1280a

Overview

Group
SmallGroup(1280,1035864)
Rank
5
Schläfli Type
{4,40,2,2}
Vertices, edges, …
4, 80, 40, 2, 2
Order of s0s1s2s3s4
40
Order of s0s1s2s3s4s3s2s1
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

16-fold

20-fold

40-fold

Covers minimal covers in bold

None in this atlas.

Representations

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