Polytope of Type {24,4} with group SmallGroup(1920,240809)

Overview

Group: SmallGroup(1920,240809)
Rank: 3
Schläfli Type: {24,4}
Vertices, edges, …: 240, 480, 40
Order of s₀s₁s₂: 20
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

{6,4}*120

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s1*s2*s1*s0*s2> of order 2

20 facets

20 of {24}*48

120 vertex figures

120 of {4}*8

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 3

16 facets

12 of {24}*48
4 of {8}*16

80 vertex figures

80 of {4}*8

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 6

8 facets

6 of {24}*48
2 of {8}*16

40 vertex figures

40 of {4}*8

Representations

Permutation Representation (GAP)

s0 := ( 1,27)( 2,28)( 3,35)( 4,36)( 5,50)( 6,49)( 7,46)( 8,45)( 9,34)(10,33)(11,52)(12,51)(13,43)(14,44)(15,38)(16,37)(17,31)(18,32)(19,30)(20,29)(21,42)(22,41)(23,39)(24,40)(25,47)(26,48);;
s1 := ( 1,27)( 2,28)( 3,31)( 4,32)( 5,35)( 6,36)( 7,39)( 8,40)( 9,41)(10,42)(11,37)(12,38)(13,46)(14,45)(15,49)(16,50)(17,34)(18,33)(19,51)(20,52)(21,47)(22,48)(23,29)(24,30)(25,43)(26,44);;
s2 := ( 1,28)( 2,27)( 3,35)( 4,36)( 5,48)( 6,47)( 7,46)( 8,45)( 9,42)(10,41)(11,30)(12,29)(13,37)(14,38)(15,44)(16,43)(17,32)(18,31)(19,52)(20,51)(21,34)(22,33)(23,40)(24,39)(25,49)(26,50);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(52)!( 1,27)( 2,28)( 3,35)( 4,36)( 5,50)( 6,49)( 7,46)( 8,45)( 9,34)(10,33)(11,52)(12,51)(13,43)(14,44)(15,38)(16,37)(17,31)(18,32)(19,30)(20,29)(21,42)(22,41)(23,39)(24,40)(25,47)(26,48);
s1 := Sym(52)!( 1,27)( 2,28)( 3,31)( 4,32)( 5,35)( 6,36)( 7,39)( 8,40)( 9,41)(10,42)(11,37)(12,38)(13,46)(14,45)(15,49)(16,50)(17,34)(18,33)(19,51)(20,52)(21,47)(22,48)(23,29)(24,30)(25,43)(26,44);
s2 := Sym(52)!( 1,28)( 2,27)( 3,35)( 4,36)( 5,48)( 6,47)( 7,46)( 8,45)( 9,42)(10,41)(11,30)(12,29)(13,37)(14,38)(15,44)(16,43)(17,32)(18,31)(19,52)(20,51)(21,34)(22,33)(23,40)(24,39)(25,49)(26,50);
poly := sub<Sym(52)|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, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.