Nonorientable 3-manifolds admitting coloured triangulations with at most 30 tetrahedra

TL;DR

This paper provides a comprehensive census of non-orientable, closed 3-manifolds that can be represented with coloured triangulations of up to 30 tetrahedra, using computational methods.

Contribution

It introduces a complete enumeration of such manifolds through computer-generated crystallizations, expanding the understanding of their combinatorial structures.

Findings

Census of all non-orientable 3-manifolds with ≤30 tetrahedra

Development of algorithms for generating and comparing crystallizations

Identification of all rigid non-bipartite crystallizations within the size limit

Abstract

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.