Imaginary Cubes

  • Imaginary Cube Puzzle 3H=6T (Will soon be) available from Kyoto University Museum Shop Musep
    Imaginary Cube Puzzle 3H=6T (by Musep)

    Imagine a three dimensional object which has square projections in three orthogonal directions, as the figure shows. A cube has this property, but it is not the only answer and there are plenty of examples like a regular tetrahedron and a cuboctahedron. Note that a regular tetrahedron looks square from each of its edges, because a tetrahedron is obtained by selecting every other vertices of a cube.

    From an object with this property, one can imagine a cube which has the same three square projections. Therefore, we call such an object an Imaginary Cube ( I-cube in short). I have been studying about Imaginary Cubes and found many interesting objects, in particular when it has a fractal structure. In order to convey this mathematical surprize, I have made some mathematical sculptures.

    Please enjoy them.


    Mathematical Sculptures



    Java Applet

    Fractal Imaginary Cubes
    Rotate and examine with a Java applet!


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