Golyhedron update

Alexey Nigin has discovered a 15-face golyhedron, a vast improvement on my 32-face example. The optimisation was effected by the idea to only have a single club foot, and merely truncate the other end.

alexeyhedron

 

The smallest golyhedron therefore has either 11, 12 or 15 faces. Can you reduce Alexey’s upper bound even futher by finding an 11- or 12-faced golyhedron, or increase my lower bound by proving the impossibility thereof?

Make your own golyhedron

The faces of Alexey’s golyhedron can be orientation-preservingly juxtaposed into a 15-by-8 rectangle:

tiles

You can download and print an Alexeyhedron template to assemble your own model of the 15-face golyhedron. I bodged together an example from card and Sellotape; I’m sure that you could do better than this:

VLUU L200  / Samsung L200

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5 Responses to Golyhedron update

  1. Sam says:

    In your image of the Alexeyhedron, the arm connecting to the club foot should be one cube shorter.

  2. Alexey Nigin says:

    I have found a 12-faced golyhedron!

    http://yadi.sk/d/dmqoxL8kR6fSC

  3. Alexey Nigin says:

    I have just discovered an 11-faced golyhedron!
    Here is its diagram:

    1111111
    15
    15

    A picture can be downloaded from https://yadi.sk/d/Zzw_Q6gKTZjwk.

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