I have been playing with Pentominoes for more than 30 years and I never thought about Quadrominoes, so here goes.
You can either use alphabet blocks like what I did on the Pentominoes Instructable
or you can buy plain wooden cubes which come in various sizes. Or buy a square stick available at lumber yards or craft stores and cut your own. The important part is that the cubes are are uniformly the same size.
You will need 64 cubes or if you start with a stick, the equivalent of 64 cubes.
You will need glue and rubber bands. Paint is optional but fun.
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Step 1: Creating the Pieces
There are eight 3-D shapes that can be made from four cubes. Left, Corner, Right, L-shaped, Square, I-shaped, T-shaped and Zig-zag. Eight pieces times four cubes each is 32 cubes which is OK but when you double that and get 64 cubes, you can make a 4x4x4 cube plus various other shapes.
Make two of each of these shapes for a total of 16 pieces.
Glue the cubes into these shapes and user rubberbands to hold them together until dry.
Step 2: Optional - Paint
Paint the shapes as you see fit.
Step 3: Making Shapes
- 4x4x4 cube
- 2x4x8 solid rectangle
- two 2x4x4 solid rectangles
- four 2x2x4 solid rectangles
- a shape I call the Cathedral