A tesseract has 16 corners, 32 edges, 24 square faces, and 8 cube cells. Every edge here is real; what isn't real is the flattening — four dimensions can't fit on a screen.
So the image is a projection: the bright outer cube and dim inner cube are two of the eight cells, the inner one pushed "inward" because it sits farther along the 4th axis. Slide 4D depth and watch it turn inside-out as the shadow re-casts.
The two violet dots sit at mirror-image corners — the pattern (+,−,−,+) read off 6·0·0·6, and its exact opposite through the center — joined by the tesseract's long diagonal. A point and its reflection, the two-dots theme carried into 4D.
An honest nugget the 6 nods at: 4D rotation genuinely has six independent planes (xy, xz, xw, yz, yw, zw) — a cube only has three. That sixfold freedom is why a tesseract can tumble in ways a cube never could.