Polytope of Type {4,18} with group SmallGroup(144,41)

Overview

Group: SmallGroup(144,41)
Rank: 3
Schläfli Type: {4,18}
Vertices, edges, …: 4, 36, 18
Order of s₀s₁s₂: 36
Order of s₀s₁s₂s₁: 2
Also known as: {4,18|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

{2,18}*72

3-fold

{4,6}*48a

4-fold

{2,9}*36

6-fold

{2,6}*24

9-fold

{4,2}*16

12-fold

{2,3}*12

18-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References