Polytope of Type {8,80} with group SmallGroup(1280,82982)

Overview

Group: SmallGroup(1280,82982)
Rank: 3
Schläfli Type: {8,80}
Vertices, edges, …: 8, 320, 80
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

Quotients maximal quotients in bold

2-fold

{8,40}*640d

4-fold

5-fold

{8,16}*256b

8-fold

10-fold

{8,8}*128c

16-fold

20-fold

32-fold

{2,10}*40

40-fold

64-fold

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

Permutation Representation (Magma)

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

References