perplexus.info :: Shapes : TetraCubes

TetraCubes (Posted on 2007-05-08)

The following are the 8 tetracubes which can be made by combining 4 cubes. In all, 32 unit cubes are used. That would form two layers of a 4x4x4 cube.

If you are able to use each tetracube once to form this arrangement I'd be pleased to receive your solution. If it can't be done indicate why.

Note: in the graphic F4, G4 and H4 are above the cubes that form the lower layer. Also, the G and H tetracubes 'screw' one to the left and the other to the right.

A solution might take the form of 2 4x4 grids using letters only; numerals really only assist in orienting oneself.

Submitted by brianjn

Rating: 4.0000 (3 votes)

Solution: (Hide)

Pencil and paper was too confusing so I cut and glued my tetracubes together out of wood.

My arrangement was:

Lower layer: Top layer: G1 F3 F1 H3 G3 G4 F4 H1 G2 E4 F2 B4 C1 C4 H4 H2 E1 E2 E3 B3 C2 D1 D2 B2 A1 A2 A3 A4 C3 D3 D4 B1

The numbering is not an issue, all that is required is to have the appropriate letter in place and realise that two layers are involved.

A 90 degree anticlockwise rotation of the F block creates a mirror image.

Clearly there will be rotations and reflections.

Given two sets of these tetracubes the two layers of one, like above, can "marry" across the 2nd and 3rd layers thus providing more diversity. I have not investigated that.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-09-01 09:27:18
re: Found one	brianjn	2007-05-10 19:42:59
Found one	Jer	2007-05-09 12:25:58

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