The Relationship Between Penrose Triangle and Toroidal Impossible Object of Square Prisms

This study introduces the concept of the “Toroidal Impossible Object of Square Prisms” (referred to as TIOSP), which satisfies specific conditions among impossible objects constructed from square prisms. The author’s focus is exclusively on analyzing TIOSP. To achieve this, the author treats TIOSP as realistic objects by representing them with 3D vectors in mathematics. Through experimentation, this study shows that each TIOSP can be transformed into a Penrose triangle using vector sum operations. Furthermore, the author demonstrate that the side lengths of the transformed Penrose triangle can be determined by examining the discontinuity length of the original TIOSP. Based on these findings, Based on these findings, the author aims to specify the conditions to establish clear criteria for TIOSP. This study validates this approach through experiments using the “TIOSP Transforming 3D CG System,” developed by the author.