Polytope of Type {8,6} with group SmallGroup(1920,240844)

Overview

Group: SmallGroup(1920,240844)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 160, 480, 120
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 12
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

120-fold

{4,2}*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*s2*s1*s0*(s1*s2)^2*(s1*s0*s1*s2)^2> of order 2

60 facets

60 of {8}*16

80 vertex figures

80 of {6}*12

P/N, where N=<s2*s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 3

40 facets

40 of {8}*16

64 vertex figures

48 of {6}*12
16 of {2}*4

P/N, where N=<(s0*s2*s1)^4> of order 5

24 facets

24 of {8}*16

32 vertex figures

32 of {6}*12

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

20 facets

20 of {8}*16

32 vertex figures

24 of {6}*12
8 of {2}*4

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.