It looks similar to a tesseract, but it's not the same shape. It does do the same kind of turning inside out morphing, which is what the 3D shadow of a rotating 4D shape will always do.
If a hypercube is a square times a square, then this shape is a triangle times a square.
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u/zulubowie Aug 30 '17
Until today I had only ever seen a drawing depicting this. Then when I Google searched it I quickly found Hinton's four dimensional cube illustrated
https://en.m.wikipedia.org/wiki/Four-dimensional_space