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

Overview

Group: SmallGroup(1920,240844)
Rank: 3
Schläfli Type: {20,8}
Vertices, edges, …: 120, 480, 48
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

{5,4}*120

120-fold

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

Permutation Representation (Magma)

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

References