Polytope of Type {6,8} with group SmallGroup(1440,4612)

Overview

Group: SmallGroup(1440,4612)
Rank: 3
Schläfli Type: {6,8}
Vertices, edges, …: 90, 360, 120
Order of s₀s₁s₂: 15
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{6,4}*720

3-fold

{6,8}*480b

6-fold

{6,4}*240c

12-fold

{6,4}*120

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

44 facets

38 of {6}*12
6 of {2}*4

30 vertex figures

30 of {8}*16

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

24 facets

24 of {6}*12

18 vertex figures

18 of {8}*16

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.