Ever since reading George Gamow's popular science book as a teenager, I have thought his diagram of a hypercube/tesseract was an artist's impression.
Today I learned that this image is the result of calculating a perspective projection of a transparent unit hypercube from a distance of 2.5. You are looking from quite near the hypercube so perspective is exaggerated.
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As the distance of the viewer from the hypercube increases the inner and outer cube would appear to converge. By measuring the relative sizes of the inner and outer cube one may calculate how far one is from the cube.
If the hypercube were opaque how many of the faces could one see? It depends on whether or not one has rotated in the fourth dimension. If yes, then four. If no, then three.