Polytope of Type {80,8} with group SmallGroup(1280,82962)

Overview

Group: SmallGroup(1280,82962)
Rank: 3
Schläfli Type: {80,8}
Vertices, edges, …: 80, 320, 8
Order of s₀s₁s₂: 80
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie

Quotients maximal quotients in bold

2-fold

{40,8}*640d

4-fold

5-fold

{16,8}*256a

8-fold

10-fold

{8,8}*128a

16-fold

20-fold

32-fold

{10,2}*40

40-fold

64-fold

{5,2}*20

80-fold

160-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References