Polytope of Type {8,20} with group SmallGroup(1920,240844)

Overview

Group: SmallGroup(1920,240844)
Rank: 3
Schläfli Type: {8,20}
Vertices, edges, …: 48, 480, 120
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

{4,5}*120

120-fold

{2,4}*16

240-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 := ( 1,38)( 2,33)( 3,21)( 4,36)( 5,19)( 6,34)( 7,17)( 8,22)( 9,32)(10,16)(11,30)(12,26)(13,20)(14,39)(15,37)(18,23)(24,40)(25,35)(29,31);;
s1 := ( 1, 7)( 2,36)( 4,26)( 5,17)( 6,38)( 8,16)( 9,30)(10,29)(11,20)(13,21)(14,34)(15,33)(18,40)(19,24)(22,27)(23,35)(25,39)(28,31)(42,44);;
s2 := ( 1,15)( 2, 4)( 3,14)( 5, 9)( 6,31)( 7,35)( 8,24)(11,30)(12,18)(13,20)(17,25)(19,32)(21,39)(22,40)(23,26)(29,34)(33,36)(37,38)(41,44)(42,43);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(44)!( 1,38)( 2,33)( 3,21)( 4,36)( 5,19)( 6,34)( 7,17)( 8,22)( 9,32)(10,16)(11,30)(12,26)(13,20)(14,39)(15,37)(18,23)(24,40)(25,35)(29,31);
s1 := Sym(44)!( 1, 7)( 2,36)( 4,26)( 5,17)( 6,38)( 8,16)( 9,30)(10,29)(11,20)(13,21)(14,34)(15,33)(18,40)(19,24)(22,27)(23,35)(25,39)(28,31)(42,44);
s2 := Sym(44)!( 1,15)( 2, 4)( 3,14)( 5, 9)( 6,31)( 7,35)( 8,24)(11,30)(12,18)(13,20)(17,25)(19,32)(21,39)(22,40)(23,26)(29,34)(33,36)(37,38)(41,44)(42,43);
poly := sub<Sym(44)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2 >;

References