Polytope of Type {9,9} with group SmallGroup(648,703)

Overview

Group: SmallGroup(648,703)
Rank: 3
Schläfli Type: {9,9}
Vertices, edges, …: 36, 162, 36
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 3
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

27-fold

{3,3}*24

Covers minimal covers in bold

2-fold

3-fold

{9,9}*1944c

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)^3> of order 3

18 facets

9 of {3}*6
9 of {9}*18

18 vertex figures

9 of {9}*18
9 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.