Provide a theoretical description of a tesseract (hypercube) as a four-dimensional analog of a cube. Explain how it is constructed by extending a cube into a fourth spatial dimension. Describe the relationship between a point, a line, a square, a cube, and a tesseract. Discuss how a 4D object might cast a 3D shadow and attempt to describe what a 3D being might perceive if a tesseract were to pass through their plane of existence.