Polytope of Type {24,6} with group SmallGroup(1440,4612)

Overview

Group: SmallGroup(1440,4612)
Rank: 3
Schläfli Type: {24,6}
Vertices, edges, …: 120, 360, 30
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{12,6}*720a

3-fold

{8,6}*480b

6-fold

{4,6}*240c

12-fold

{4,6}*120

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

Permutation Representation (Magma)

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

References