In this article we analyse 3D models of cultural heritage with the aim of answering three main questions: what processes can be put in place to create a FAIR-by-design digital twin of a temporary exhibition? What are the main challenges in applying FAIR principles to 3D data in cultural heritage studies and how are they different from other types of data (e.g. images) from a data management perspective? We begin with a comprehensive literature review touching on: FAIR principles applied to cultural heritage data; representation models; both Object Provenance Information (OPI) and Metadata Record Provenance Information (MRPI), respectively meant as, on the one hand, the detailed history and origin of an object, and - on the other hand - the detailed history and origin of the metadata itself, which describes the primary object (whether physical or digital); 3D models as cultural heritage research data and their creation, selection, publication, archival and preservation. We then describe the process of creating the Aldrovandi Digital Twin, by collecting, storing and modelling data about cultural heritage objects and processes. We detail the many steps from the acquisition of the Digital Cultural Heritage Objects (DCHO), through to the upload of the optimised DCHO onto a web-based framework (ATON), with a focus on open technologies and standards for interoperability and preservation. Using the FAIR Principles for Heritage Library, Archive and Museum Collections [1] as a framework, we look in detail at how the Digital Twin implements FAIR principles at the object and metadata level. We then describe the main challenges we encountered and we summarise what seem to be the peculiarities of 3D cultural heritage data and the possible directions for further research in this field.