Polytope of Type {6,9} with group SmallGroup(432,521)

Overview

Group: SmallGroup(432,521)
Rank: 3
Schläfli Type: {6,9}
Vertices, edges, …: 24, 108, 36
Order of s₀s₁s₂: 36
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{6,3}*144

4-fold

{6,9}*108

9-fold

{6,3}*48

12-fold

18-fold

{3,3}*24

36-fold

{2,3}*12

Covers minimal covers in bold

2-fold

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

18 facets

18 of {6}*12

12 vertex figures

12 of {9}*18

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

18 facets

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

8 vertex figures

8 of {9}*18

P/N, where N=<s0*s1*s2*(s1*s0)^2*s2*s1> of order 4

9 facets

9 of {6}*12

6 vertex figures

6 of {9}*18

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.