The annual international Bridges Conference is the preeminent meeting on the connections between mathematics and art, music, architecture, education and culture. Bridges 2022 was held at Aalto University and Helsinki University in Espoo and Helsinki, Finland. This five-day conference included invited and contributed talks, workshops, a juried art exhibition, musical performances, a short film festival, a poetry reading and family day.

This article focuses on the shape of the vaults that cover the rooms of the Fort of Umm al-Dabadib (Kharga Oasis, Egypt's Western Desert), dating to the Late Roman Period. This building is the central element of the contemporary Fortified Settlement, consisting of a dense, three-dimensional mosaic of domestic units, all covered by similar vaults, and belonging to a chain of similar installations. Two elements make Umm al-Dabadib an interesting case-study: the excellent preservation of its architectural remains, and the possibility to rely on an accurate photogrammetric survey of the entire built-up area. Thanks to this combination, it was possible to analyse the geometric shape of the vaults in connection to the ancient building techniques. The study determined that the vaults of the Fort are elliptical; this conclusion will impact on the study of all the similar settlements built in the Kharga Oasis, and possibly to other contemporary buildings elsewhere in Egypt.

Editor-in-Chief Kim Williams examines the sometimes very sophisticated use of fundamental mathematical elements-curves, grids, simple polygons and polyhedra-in ancient and contemporary architecture and introduces the articles in vol. 23 no. 3 (2021).

This paper presents a teaching experiment in which 3D digital computational models are explored as the representational base to integrate formal, structural, and environmental performance criteria in design. By describing the academic experience, the paper reflects on its methodologies and results, as well as on the relation between human and computer factors in the design process. This assessment is important to make the students aware of the increasingly intelligent design systems offered by digital technologies to support architectural design, as well as of their relationship with precedent digital and analog representational mediums.

The digital paradigm requires efficient methods of teaching CAAD tools in architecture schools. With the trend of enhancing the design process with parametric methods, linking architecture with other knowledge areas, such as mathematics, is gaining in importance. Equipping future architects with skills in algorithmic thinking is yet another challenge for education. This paper describes the workflow of an early-stage course addressing this challenge, conducted at the Warsaw University of Technology's Faculty of Architecture. The course focuses on the students' ability to construct complex geometric forms in the digital environment by introducing an extensive analytic phase. The students study the geometric foundations of real-world architectural cases and translate them into parametric models. Later, they explore the potential of the generated solutions space. The results compare the course's teaching efficiency with the outcomes of past courses covering similar subjects.

This paper reflects upon the remarkable ceiling of the Picasso Museum in Malaga, an example of the wooden coffered ceilings built during the early Renaissance in Spain. The unusual design of the ceiling is based on octagons surrounded by four-pointed stars. This is used as the point of departure for a mathematical investigation of polyhedral forms. Two different polyhedra are constructed, conceived in such a way that the honeycombs generated by them, can be considered a polyhedral generalization of the planar pattern of regular octagons and four-pointed stars. Both are constructed by means of special truncations of a cube. The truncation procedure is extended to construct a polyhedral generalization of the planar pattern of four-pointed stars and 45° rhombuses; in this case, the polyhedron obtained is a variation of one of the star polyhedra drawn by Jamnitzer. The geometric honeycombs thus defined could be used as models for new designs.

This letter from the editors commences by reporting on Nexus 20/21, the 13th international, interdisciplinary conference for architecture and mathematics. This event took place in July 2021 as an online conference. From over 50 presentations at the conference, the Scientific Committee nominated a series of works for potential inclusion in two special issues of the This letter introduces eleven papers selected for Vol. 24(2), with the remainder to appear in Vol. 24(3).