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

Overview

Group: SmallGroup(1920,240844)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 120, 480, 160
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

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

80 facets

80 of {6}*12

60 vertex figures

60 of {8}*16

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

64 facets

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

40 vertex figures

40 of {8}*16

P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*s1> of order 5

32 facets

32 of {6}*12

24 vertex figures

24 of {8}*16

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

32 facets

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

20 vertex figures

20 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.