Polytope of Type {12,9} with group SmallGroup(648,703)

Overview

Group: SmallGroup(648,703)
Rank: 3
Schläfli Type: {12,9}
Vertices, edges, …: 36, 162, 27
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

27-fold

{4,3}*24

Covers minimal covers in bold

2-fold

3-fold

{12,9}*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)^4> of order 3

15 facets

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

12 vertex figures

12 of {9}*18

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.