This article presents a methodology for modeling and manufacturing three-dimensional (3D) geometric figures. The need for developing the methodology is substantiated, and its significance for the STEM training of future specialists in engineering specialties is demonstrated. An advantage of the methodology is the clear structuring of all its stages, levels, and steps, which simplifies the process of implementing STEM projects. Structurally, the methodology includes a preparatory stage and four main stages. Stage 1 involves designing the object model, which includes collecting information about its characteristics and developing a mathematical model. Based on the mathematical model, the main parameters of the investigated object (part) are determined and calculated. At Stage 2, the computer-aided construction of a three-dimensional model of the object is performed, taking into account the parameters determined at the first stage. The development of drawings and the 3D model is carried out in an appropriate software environment, in particular, in the AutoCAD computer-aided design (CAD) system. Based on the calculated parameters, different types of three-dimensional models of the object are created: wireframe, surface, and solid. Stage 3 involves the implementation of additive manufacturing, that is, the manufacture of a physical prototype of the investigated object using 3D printing. For models of significant overall dimensions or complex geometric shapes that complicate printing, preliminary decomposition of the model into separate parts is performed. After printing, the individual components are joined, and the resulting physical prototype undergoes appropriate post-processing. Stage 4 involves the validation of the  manufactured physical 3D model by assessing its conformity with the digital model of the object. Comparison of the physical and software models can be carried out based on the analysis of their photographic images using digital image processing methods. In addition, a visual assessment of the prototype and measurements of its main geometric parameters are performed. An example of the implementation of a STEM project aimed at the creation, investigation, and physical reproduction of a three-dimensional model of a small stellated dodecahedron by means of 3D printing is presented. According to the developed methodology, at the first stage, a mathematical model of the dodecahedron was developed. At the second stage, based on this model, wireframe, surface (polygonal), and solid (volumetric) models were sequentially developed. An important advantage of the proposed methodology is the step-by-step construction of the wireframe model, which begins with the construction of simple geometric primitives. At the subsequent stages, individual primitives and their groups are sequentially combined into more complex structural elements. This approach simplifies the construction process and enables the step-by-step creation of complex three-dimensional models. At the third stage, the model was decomposed, prepared for printing, and its individual components were manufactured using an FDM 3D printer. After that, the printed parts were assembled and the resulting product was post-processed. As a result, a physical model of the small stellated dodecahedron was manufactured, whose geometric dimensions and surface quality meet the requirements and objectives of the STEM project. A physical model of the small stellated dodecahedron was fabricated, with a pentagon edge length of b = 25.3 mm and a circumscribed sphere diameter of DS = 127.2 mm. The maximum dimensional deviation of the dodecahedron was 0.3 mm.