Polytope of Type {20,4} with group SmallGroup(1920,240809)

Overview

Group: SmallGroup(1920,240809)
Rank: 3
Schläfli Type: {20,4}
Vertices, edges, …: 240, 480, 48
Order of s₀s₁s₂: 24
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

{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)^3*s1*s2> of order 3

16 facets

16 of {20}*40

80 vertex figures

80 of {4}*8

P/N, where N=<(s0*s1)^4> of order 5

16 facets

8 of {4}*8
8 of {20}*40

48 vertex figures

48 of {4}*8

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

References

None.

to this polytope.