Polytope of Type {33,2} with group SmallGroup(132,9) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(132,9)
Rank: 3
Schläfli Type: {33,2}
Vertices, edges, …: 33, 33, 2
Order of s₀s₁s₂: 66
Order of s₀s₁s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

3-fold

{11,2}*44

11-fold

{3,2}*12

Covers minimal covers in bold

2-fold

{66,2}*264

3-fold

4-fold

5-fold

{165,2}*660

6-fold

7-fold

{231,2}*924

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

{429,2}*1716

14-fold

15-fold

Representations

Permutation Representation (GAP)

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