## 1 Introduction  
Lattice structures have attracted significant interest in various engineering sectors because of their high specific stiffness [1; 2; 3; 4], high specific strength [1; 2; 5; 6; 7; 8], high energy absorption [2; 5; 7; 8], fracture toughness [1; 3; 7; 8], and peculiar lightweight designs [7; 8]. Lattice designs are three-dimensional structures built up of a series of interconnecting beams, struts, or Triply Periodic Minimal Surfaces (TPMSs) [7]. They are typically used to build lightweight [8] and robust structures [7; 8] in engineering applications. Taking advantage of polygonal hollow shapes in lattice structures gives an added level of design flexibility [7; 9]. Hollow polygonal shapes, including hexagons, triangles, rectangles/squares, and circles, provide numerous benefits [7] in lattice structures. These designs have the capacity to improve the distribution of the load [2], stiffness [7], and efficient use of materials [8]. Lattice structures attract significant interest for research in structural engineering, with their importance arising from numerous primary factors, such as their good strength, lightness, and customisability [7; 8]. Lightweight structures formed from lattice structures are in substantial demand in an era where sustainability and resource efficiency are key [8; 10]. Lattice structures, particularly those built with polygonal hollow shapes, offer the rare opportunity of saving materials while maintaining the structural integrity of components [7]. Furthermore, lattice structures are ideal for use in a number of industries, including the aerospace, automotive, civil engineering, and biomedical industries, because of their inherent strength-to-weight ratio [11; 12; 13; 14; 15]. Engineers optimise the performance of their designs by analysing the use of different polygonal hollow shapes in lattice structures [10; 14; 15]. The process of designing and manufacturing lattice structures has also undergone radical changes as a result of emerging new materials and manufacturing technologies such as additive manufacturing (AM) [10; 11; 12; 13; 14; 15]. These developments have made it possible to build complex lattice structures using different polygonal hollow shapes [7; 10; 15]. Additionally, lattice structures have applications that go beyond typical structural engineering, such as transferring heat, damping for vibrations, and acoustics [8; 12; 15]. A review of their application in a number of fields provides cross-disciplinary insights from materials science, mechanical engineering, structural engineering, aerospace engineering, biomechanics, and medical engineering, as well as energy and environmental engineering, AM, computer-aided design (CAD) and computational modelling, and robotics and automation. Comprehending the analytical models for lattice structures built with different polygonal hollow shapes is critical for the optimisation of their design and prediction of their behaviour under different loads and boundary conditions [7]. Given the global trend towards reducing carbon footprints and energy consumption, lattice structures offer an eco-friendly alternative by minimising material use and allowing energy-efficient manufacturing [8; 10; 11; 12; 14; 15]. The research area of lattice structures is constantly changing with ongoing advancements and breakthroughs, such as the recently reported work integrating metamaterials into lattice parts [10]. This review attempts to shed light on present trends in structural engineering related to lattice structures and prospective future developments. This review article first provides an overview of lattice structures and the polygon hollow shapes that are used in them. This is followed by a section that examines current as well as relevant principles and methods for modelling lattice structures.