Organizing the properties of impossible figures

Area of Science:

• Cognitive Psychology
• Mathematics
• Visual Perception

Background:

• Empirical study of impossible figures requires well-specified independent variables.
• Existing classifications may not adequately partition figures for detailed analysis.

Purpose of the Study:

• To develop a formal classification system for cornered torus figures.
• To aid in the identification of formal and psychological properties of figures.
• To provide a systematic framework analogous to the periodic table.

Main Methods:

• Formal derivation of a polytopic classification system.
• Partitioning cornered torus figures into meaningful subsets.
• Development of coherent 3D and 2D representations of the system.

Main Results:

• A novel classification system for cornered torus figures is established.
• The system formally categorizes figures based on inherent properties.
• The classification is applicable to both known and unknown figures.

Conclusions:

• The developed classification system facilitates the empirical investigation of impossible figures.
• This formal system offers a structured approach to understanding figure properties.
• The polytopic system provides a comprehensive framework for visual perception research.