The 16 vertices sit at coordinates (±1,±1,±1,±1) in true 4D space. An edge exists whenever two vertices differ in exactly 1 coordinate (32 edges). Each frame the vertices are rotated by a real 4D rotation matrix, then perspective-projected into 3D by dividing by (d − w). A tesseract is made of 8 cubic "cells" (3D faces) — 2 of them (inner and outer) are highlighted here, and the faint shadow below is that same projection flattened onto the ground.
🧊 The inner and outer "cubes" are the same shape, just nearer and farther along the w axis. Rotating in 4D makes them continuously "grow" through one another — this is the real appearance of a tesseract, not an approximation.