Polytope of Type {6,24} with group SmallGroup(1920,240809)

Overview

Group: SmallGroup(1920,240809)
Rank: 3
Schläfli Type: {6,24}
Vertices, edges, …: 40, 480, 160
Order of s₀s₁s₂: 24
Order of s₀s₁s₂s₁: 20
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

{6,6}*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

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*s1*s2*s1*s0*(s2*s1)^3> of order 5

32 facets

32 of {6}*12

8 vertex figures

8 of {24}*48

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.