Building a 3-cube with the edge connected tricubes - Rubik's Mini Bricks
      Torsten Sillke - 2000-04-04

The numbering is mine the names are Rubik's.

The tricubes: face-connected

  0) o o o   Tower              o : cube on the first level
                                x : cube on the second level
  1) o       L                  y : cube on the third level
     o o
  
The tricubes: face-edge-connected
  
  figures 0 and 1 plus
  
  2) o o     Hook
         o
  
  3) o o     Diagonal L
     x
  
  5) x o     6)   o x   5=Worm Sandwich
         o      o       6=Worm Head
  
  7) o   o   Wing
       o
  
  4) o       Steps
       o
         o
  
  8) x o     Claw
     o
  
Def: x-free
  A tiling is said x-free if there is no configuration:

   a b                                     7 2 2
   b a  with a<>b.   Example for a xing: 7 2 7

Packing the 3-cube with pseudo-tricubes:
========================================
  With the tiles 0..8 it is possible to build a 3x3x3 cube x-free.
  There is a solution consists of six symmetric parts 
  0, 1, (2,7), (3,5,6), 4, 8.
  
 \       \       \
  0 8 4   0 3 7   0 3 5
  8 4 7   5 8 6   3 5 1
  4 2 2   2 6 7   6 1 1
       \       \       \


  This 3-cube packing problem has been invented by many people.
  I don't know who was the first. One of them was E. Rubik.
  He calls them Mini Bricks (copyright 1974) see http://www.rubiks.com

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References:

- S. W. Golomb; 
  Polyominoes, Princeton Univ. Press, 1994 (2nd edition).

- E. Rubik; Mini Bricks (C. 1974)
  http://www.rubiks.com