In recent years, topological photonics has emerged as an exciting research field in which topological concepts, originally introduced to understand the behaviour of electrons in solid-state materials, are instead exploited to design and control the behaviour of light . In this direction, the development of so-called 'synthetic dimensions' offers a particularly powerful approach to exploring topological photonics. The central idea of this method is to identify and couple together a set of internal degrees of freedom so as to simulate the motion of a quantum particle along an extra spatial direction . In this framework, a system with D-real dimensions can be made to behave like a D + d-dimensional system, when d synthetic dimensions are added to the system. This approach, therefore, both raises the prospect of simulating exotic systems with four or more spatial dimensions, but also provides, through the external control of couplings, a straightforward way to design topological lattices in different dimensions .