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A proper chromosome segregation between daughter cells during cell division is crucial for genome integrity. The key regulatory mechanism for this process is related to the attachments of spindle tubulin microtubules (MTs) to kinetochores. Any disturbance of this process can lead to chromosome missegregation and cause developmental disorders such as aneuploidy and cancer. Improper MT attachments to kinetochores, called merotelic, take place when MTs captured by kinetochore of one chromatid originate from both spindle poles and are considered as one of the key pathological processes on the level of cell division. In this paper, we present the first comprehensive 3D model of three consecutive stages of mitosis, namely, prometaphase, metaphase, and anaphase, as well as the results of simulating the kinetochore-MT attachments. It appears that large values of the kinetochore corona angle lead to the preservation of merotelic attachments until the anaphase while the size of the cell, the number of MTs and the probability of MT detachments affect only the rate suppression of merotelic attachments. We demonstrate that the structure and the set of parameters of the virtual cell have a severe impact on the results of computer simulations. We also compare the results of 3D modeling of mitosis with outcomes of an existing two-dimensional model as well as with some experimentally established facts.