Polytope of Type {8,6} with group SmallGroup(960,10869)

Overview

Group: SmallGroup(960,10869)
Rank: 3
Schläfli Type: {8,6}
Vertices, edges, …: 80, 240, 60
Order of s₀s₁s₂: 10
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

{4,6}*120

120-fold

{2,2}*8

Covers minimal covers in bold

2-fold

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

30 facets

30 of {8}*16

40 vertex figures

40 of {6}*12

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

20 facets

20 of {8}*16

32 vertex figures

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

P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*(s0*s2*s1)^3*s2> of order 6

10 facets

10 of {8}*16

16 vertex figures

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

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.