Observations from the 8-Tetrahedron Nonorientable Census

Abstract

Through computer enumeration with the aid of topological results, we catalogue all 18 closed nonorientable ℙ²-irreducible 3-manifolds that can be formed from eight or fewer tetrahedra. In addition, we give an overview as to how the 100 resulting minimal triangulations are constructed. Observations and conjectures are drawn from the census data, and future potential for the nonorientable census is discussed. Some preliminary 9- tetrahedron results are also included.

Keywords:

• Primary 57Q15
• Secondary 57-04, 57N10
• Minimal triangulation
• census
• complexity
• layering