Polytope of Type {12,6} with group SmallGroup(432,523)

Overview

Group: SmallGroup(432,523)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 36, 108, 18
Order of s₀s₁s₂: 3
Order of s₀s₁s₂s₁: 12
Also known as: {12,6}₃. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{12,6}*144d

4-fold

{6,6}*108

9-fold

{4,6}*48b

18-fold

{4,3}*24

Covers minimal covers in bold

2-fold

{12,6}*864b

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*s2*(s1*s0)^5*s1*s2> of order 2

12 facets

6 of {12}*24
6 of {6}*12

18 vertex figures

18 of {6}*12

P/N, where N=<(s0*s1)^4> of order 3

10 facets

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

12 vertex figures

12 of {6}*12

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.