Polytope of Type {8,12} with group SmallGroup(1920,240844)

Overview

Group: SmallGroup(1920,240844)
Rank: 3
Schläfli Type: {8,12}
Vertices, edges, …: 80, 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

{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*s2)^3*(s1*s0)^2*(s2*s1)^2*s2> of order 2

60 facets

60 of {8}*16

40 vertex figures

40 of {12}*24

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

40 facets

40 of {8}*16

32 vertex figures

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

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

20 facets

20 of {8}*16

16 vertex figures

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

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

References

None.

to this polytope.