The study presented is part of a broader line of research in which the use of Extended Reality is investigated in the field of geometry education and the exploitation of the cultural heritage related to this subject area. In this study, a Phygital Exhibition is proposed that brings together knowledge related to Catalan polyhedra: their history, geometric characteristics, methods for their construction, and cultural heritage related to them. In particular, two types of Augmented Reality marker-based applications are proposed through which to access the heritage of knowledge related to Catalan polyhedra: the Phygital Edition of Polyhedra. The Realm of Geometric Beauty by Adriano Graziotti—which constitutes a particular piece within the history of this class of polyhedra—in which the pages of the booklet are used as a collection of image targets; and a collection of “augmented physical models” of Catalan polyhedra, that is, a set of physical reproductions of Catalan polyhedra or the polyhedra from which they are generated, used as model targets of the application. The experiments conducted demonstrate how it is possible to use Augmented Reality to create multimedia devices that facilitate the understanding of three-dimensional problems and into which it is possible to convey the heritage of knowledge—always in progress—related to a given scientific topic.
Extended Reality Ante Litteram in the Ephemeral Apparatuses of Andrea Pozzo
The ephemeral apparatuses that Andrea Pozzo proposed in his treatise Perspectiva pictorum et architectorum can be considered an example of Extended Reality ante litteram. This consideration gave rise to the idea of developing some Augmented Reality experiences to introduce, to the general public, the Circular Work, one of the illusory tabernacles proposed by Pozzo for the celebration of the Forty Hours. Through Augmented Reality, in fact, one can simulate the presence of the illusory apparatus inside the church of St. Ignatius in Rome, where Pozzo himself set it up for the celebration of Holy Thursday and Good Friday, but also make visible the geometric principles underlying the illusory artifice. During the European Researchers’ Night 2023, visitors to the church of St. Ignatius were able to use different applications, of varying technical complexity, directly in the church, experiencing the illusory artifice and learning the principles that make it possible. On this occasion it was possible to verify how the illusory suggestion conveyed through Augmented Reality experiences is effective even in the case of its simplest variants.
Exploring Lorenz Stöer’s Imaginary Space Using Augmented Reality: Geometria et Perspectiva
This paper investigates the sixteenth-century woodcuts contained in Lorenz Stöer’s Geometria et Perspectiva (1567) through digital reconstruction and Augmented Reality applications. The study analyzes the perspectival logic, geometric solids, and imaginary spatial compositions represented in the engravings, aiming to understand how Stöer constructed visual worlds that oscillate between representation and illustration. By combining historical research, geometric decoding, 3D modelling, and marker-based AR, the authors propose a multimedia exhibition where visitors can explore the hidden three-dimensional spaces behind the drawings and reconstruct possible viewing systems such as perspectographs. The AR experience enables users to compare represented, perceived, and imagined spaces, transforming historical prints into interactive learning environments. The research demonstrates how AR can enhance the interpretation and dissemination of intangible cultural heritage, making complex concepts of geometry, perception, and Renaissance visual culture accessible to wider audiences.
The Renewed Existence in AR of Max Brückner’s Lost Paper Polyhedra
This study proposes the realization of an Augmented Reality museum of mathematical-physical mod-els for distinctly educational purposes and capable of explaining mathematical and geometric princi-ples. Augmented Reality, in this context, would render them accessible while interacting with their digital twins would not endanger the preservation of the originals, and furthermore, comprehension would be enhanced thanks to the inclusion of explanatory contents. Following the teaching course proposed from our experience, it is possible to build the replica of one’s paper mock-up, thus giving pedagogical value back to the mathematical models otherwise precluded when musealized in a show-case or, worse, safeguarded in storerooms due to limited exhibition space. The first trials concern Max Brückner’s collection of polyhedra models, published in 1900 in Vielecke und Vielflache: Theorie und Geschichte, which offers the opportunity to evaluate the potentials of Augmented Reality to renew existence to a collection that is now lost.