Polytope of Type {2,4,20} with group SmallGroup(320,1159)

Overview

Group: SmallGroup(320,1159)
Rank: 4
Schläfli Type: {2,4,20}
Vertices, edges, …: 2, 4, 40, 20
Order of s₀s₁s₂s₃: 20
Order of s₀s₁s₂s₃s₂s₁: 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

{2,2,10}*80

5-fold

{2,4,4}*64

8-fold

{2,2,5}*40

10-fold

20-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;