## 1 Introduction  
Materials used in electricity are classified as conductors, insulators, and semiconductors. All elements with eight or more electrons in the outer orbits of their atoms are called insulators. Insulator materials are found in solid, liquid, and gaseous forms. Solid insulator materials are classified as organic, inorganic, and polymer insulators [1]. The behavior of insulating materials under operating conditions is an important feature to be considered in low-voltage and high-voltage applications [2, 3, 4]. In electrical circuits, solid insulators are frequently utilized as components to offer insulation, mechanical support, and to keep conductors separated [5, 6]. However, in high-voltage applications like electrical installations and power grid transmission, the electric field distribution across the surface of solid insulators often becomes highly non-uniform. This is especially true in three-phase connections, where the maximum electric field strength (E\({}_{\text{max}}\)) can result in charge accumulation or partial discharge [5, 7]. In such high-voltage applications, insulation is the most critical element to be considered, as is the applied voltage value [7, 8]. In this context, insulation coordination is the mutual compatibility of various insulation levels and protection levels in order to avoid the damage caused by overvoltages. A significant proportion of faults occurring in power systems are due to insulation problems. With developing technology, on-site and instant production has become possible. An advantage of this situation is that insulation materials can also be produced with the help of this technology. Rapid prototyping is commonly known as three-dimensional (3D) printing [9]. Three-dimensional printing technology is a tool that rapidly creates objects by layering materials according to digital model data, achieving this through a continuous process of layer-by-layer stacking and printing [10]. The first additive manufacturing process was developed by [PERSON] in 1986. Three-dimensional printing is favored for producing functional prototypes and small batches due to its rapid production capability. Moreover, certain geometric features of objects can only be achieved through additive manufacturing [11]. Three-dimensional printing technology is increasingly being incorporated into and integrated with various industries and fields [12]. This technology reduces material waste in the production of complex parts, the creation of innovative electronic devices, industrial design, model manufacturing, architectural design, jewelry, toys, ceramics, the aerospace, education, clothing industries, and medical fields, making it a valuable tool for various industries [9; 13; 14; 15; 16; 17]. Three-dimensional printing technology is affected by printer cost, the raw materials used, structure, and performance [18]. It is very important to evaluate the insulation coordination in the insulating materials produced with 3D printing technology. It is necessary to examine the faults that may occur in the dielectric material and to reveal its characteristics by analyzing the material behavior [19]. Research on dielectric breakdown mechanisms has been ongoing for years in terms of theoretical and experimental studies [20; 21; 22; 23]. Considering the reliable operation of devices and high-voltage equipment needed in the electrical and electronics industry, failures of insulation materials due to aging and wear are inevitable. Experimentally, it has been observed that the strength of solid insulation materials to electrical breakdowns varies depending on the type of material, dimensions, and applied voltage [24]. In addition, it has been emphasized in studies that factors such as ambient temperature and humidity, which determine the working conditions, should also be taken into account [25]. There are various methods for determining the breakdown strength of solid insulating materials. These methods have applications for different voltage types by IEC-60243 and IEC-60060 standards [26; 27].