Tesseract is the 4D analog of a cube: 16 vertices, 32 edges, 24 square faces, 8 cubic cells.
To visualize it, we rotate in 4D (using 6 independent rotation planes: XY, XZ, XW, YZ, YW, ZW), then project to 3D (perspective or orthographic), then project again to 2D.
The w-coordinate (4th dimension) determines color — watch how colors shift as the tesseract rotates through 4D.
Inner cube = outer cube in 4D, connected by 8 "cubic" cells.