Polytope of Type {2,20,4,2} with group SmallGroup(640,19674)

Overview

Group: SmallGroup(640,19674)
Rank: 5
Schläfli Type: {2,20,4,2}
Vertices, edges, …: 2, 20, 40, 4, 2
Order of s₀s₁s₂s₃s₄: 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

{2,10,2,2}*160

5-fold

{2,4,4,2}*128

8-fold

{2,5,2,2}*80

10-fold

20-fold

{2,2,2,2}*32

Covers minimal covers in bold

2-fold

3-fold

Representations

Permutation Representation (GAP)

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