Variations and Generalizations

  • Christoph Bandelow


By means of a slight modification every Magic cube can be transformed into a “Supercube”, a puzzle with over 2000 times as many positions. In the first section of this chapter we give a solution for the supercube and a suitable mathematical model. In the second, we pay our respects to an over one hundred year old predecessor of the Rubik’s cube. We present a possibly new and certainly very simple proof of the main theorem of Sam Loyd’s 15-Puzzle. Most of the objects treated in the third section are no longer cube-shaped, but due to a technical and structural kinship, they are all part of our science of cubology: We are talking of magic polyhedrons of all kinds.


Empty Space Equilateral Triangle Start Position Internal Angle Regular Polyhedron 
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Copyright information

© Birkhäuser Boston 1982

Authors and Affiliations

  • Christoph Bandelow
    • 1
  1. 1.Bochum-StiepelFederal Republic of Germany

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