TetraCubes

A TetraCube is a solid shape made by joining four identical cubes together, face to face.

### The Problems:

A.     Use four cubes (dice work well enough if you have them), and a systematic approach, to find as many different tetracube solids as you can. Then draw them on Isometric paper.

B.     Which two tetracubes will fit together to make a 2 by 2 by 2 cube ?

C.    Which four tetracubes will fit together to make a 2 by 2 by 4 cuboid ? There may be several ways to do this …

D.    Can you see how to put 6 of these together, with a ‘tri-cube’ to make up the volume to 27 units, to make the 3 by 3 by 3 ‘Soma’ Cube ? You can use any of the tetracubes you have found, and either of the tri-cube possibilities…

The Big One

The total volume of all 8 tetracubes is the same as that of a single ‘double-size’ tetracube. Is it possible to actually make such a solid out of the 8 smaller pieces ? First, you will have to decide which tetracube is the most likely candidate for construction… Good luck !

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