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A projected image of a Sierpinski tetrahedron has a positive measure if andonly if the images O, P, Q, R of the four vertices satisfy pOP + qOQ + rOR = 0for odd integers p, q, r. This fact was essentially obtained by Kenyon(Symbolic dynamics and its applications 135, 1992). We reformulate his proofthrough the notion of projection of differenced radix expansion sets and obtainsimilar results for other fractal objects. Specifically, we study projectionsof H-fractal and T-fractal as well as Sierpinski tetrahedron, which are fractalimaginary cubes (i.e., fractal objects that are projected to squares alongthree orthogonal directions just as a cube) of the first two degrees, andcharacterize the directions from which these fractals are projected to setswith positive measures.

Projected images of the Sierpinski tetrahedron and other fractal imaginary cubes