Polytope of Type {80,2} with group SmallGroup(320,529)

Overview

Group: SmallGroup(320,529)
Rank: 3
Schläfli Type: {80,2}
Vertices, edges, …: 80, 80, 2
Order of s₀s₁s₂: 80
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{40,2}*160

4-fold

{20,2}*80

5-fold

{16,2}*64

8-fold

{10,2}*40

10-fold

{8,2}*32

16-fold

{5,2}*20

20-fold

{4,2}*16

40-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

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

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

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