You gotta think outside the hypercube

A deep dive into the tesseract (4D hypercube) from first principles, covering how to mathematically model its edges and vertices, define 4D rotations, and project it onto a 2D screen. Multiple projection methods are explored and compared: cavalier, cabinet, isometric, rectilinear one-point perspective, fisheye perspective, and a mixed isometric+vanishing-point approach. Each method's visual strengths and distortions are analyzed with rendered animations, culminating in practical MATLAB code for generating the visualizations.