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

Overview

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

{4,6}*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=<s1*(s2*s1*s0)^3*s2*s1*s2> of order 2

120 facets

120 of {4}*8

20 vertex figures

20 of {24}*48

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

80 facets

80 of {4}*8

16 vertex figures

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

P/N, where N=<(s1*s0*s1*s2)^2, s1*(s2*s1*s0)^3*s2*s1*s2> of order 6

40 facets

40 of {4}*8

8 vertex figures

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

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

References

None.

to this polytope.