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

Overview

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

{6,4}*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*s1*s0)^3*s2*s1*s2> of order 2

40 facets

40 of {6}*12

30 vertex figures

30 of {8}*16

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

32 facets

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

20 vertex figures

20 of {8}*16

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

16 facets

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

10 vertex figures

10 of {8}*16

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

References

None.

to this polytope.