Polytope of Type {6,5} with group SmallGroup(480,948)

Overview

Group: SmallGroup(480,948)
Rank: 3
Schläfli Type: {6,5}
Vertices, edges, …: 48, 120, 40
Order of s₀s₁s₂: 8
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,5}*240a

4-fold

{6,5}*120a

Covers minimal covers in bold

2-fold

{6,10}*960a

3-fold

4-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

16 facets

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

16 vertex figures

16 of {5}*10

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.