## 1 Introduction  
The notion of topological interlocking assembly (TIA) was introduced by [PERSON] and [PERSON] to material science in 2001. Since then, architecture has embraced it, where its structural, aesthetic, and spatial potentials have been interpreted and explored [1, 2, 3, 4, 5, 6]. This assimilation has accelerated TIA's research, development, and applicability. This paper argues that TIA is particularly significant for computational architecture and identifies two key potentials of its inherent behavior: as an educational research tool and as a material system. The first potential reflects the increased educational relevance of computational architecture, evident in the current curriculum of several leading architectural schools, such as MIT [7], Royal Danish Academy [8], UCL [9], and EPFL [10], which have shifted their focus towards this area. This shift reflects a broader rethink and critical reconsideration of digital technology in the architectural design process, aiming to enhance the current state of the art [11, 12]. Within this shift, [PERSON] [13] successfully engaged TIA geometrical investigations in a design studio, providing an experimental educational platform for students to develop computational design processes through hands-on investigations. Building on this research, this paper presents a pedagogical methodology designed to further exploit the educational benefits of TIA geometric investigations. However, the limited examples of the use of TIA in computational educational contexts necessitated a trial-and-error approach to develop the methodology, highlighting a research gap that this paper addresses. The second potential engages the TIA constituent geometric relationships. A TIA is defined by an identical configuration of its elements, their mutual arrangement, and a boundary constraint that holds the whole assembly together [14] (Figure 1a). Elements' configuration necessitates the alternating rotation of their contact faces to generate the interlocking principle (Figure 1b). In this way, the arrangement of elements in TIA imposes local kinematic constraints, uniquely keeping each element locked in its position solely by the geometrical constraints of its adjacent elements. This distinctive feature, except for the elements at the assembly's periphery, prevents the removal of each element by either upward, downward, sideways, or rotational displacement by its neighbors [14]. In short, a TIA works as a system of geometries and geometric interdependencies from which the assembly's form emerges. This approach parallels computational architecture, which treats form as an emergent outcome of a system. Computational design processes abandon the traditional Modernist linear approach where the form and its aesthetic dictate structure and material choices. Instead, they synthesize the form from spatial, structural, and material principles [15]. Thus, the focus is not on the manifested form, that which appears, but on the material system from which the form emerges. The material system is an interaction between internal rules that embed the form and external morphogenetic pressures activated by contextual feedback [16]. The computational architectural theoretical discourse lacks recognition of the link between TIA and the material system, representing the second research gap that this paper addresses. With the proposed methodology, this paper aims to contribute to the practical and methodological discourse in architectural education. Firstly, by focusing on TIA's constituent geometries, the methodology seeks to expand students' spatial skills. Furthermore, the methodology's integration of computational theory and experimentation enables students to assimilate unfamiliar concepts, such as TIA, within their design processes and enhance their creative thinking [17]. Finally, this paper discusses the methodology's advantages and limitations, emphasizing a critical perspective as intrinsic to the computational approach [18].