Stack ’em up: Tetromino bookshelves

The Math

A tetromino is formed by combining four units of equal size arranged in different formations. The large square, for example, is just four units arranged in a 2 x 2 formation. The long rectangle is formed by stacking the four units one on top of the other.

To build this shelf system, you simply need to select the dimension of your base unit, then build from there. My base unit is a 10" x 10" square; if I were to do it again, I would use an 8" x 8" square. The 8" unit would make for more efficient use of materials. Once you’ve settled on the base unit size, work out the dimensions required for each tetromino shape you want to build.

All of the side pieces have mitres cut on their ends, but there’s something important to keep in mind. Any piece that has mitred ends that are not parallel to one another is cut to the base measurement (or multiples of the base measurement) you’ve chosen. In my case, this is 10". But any piece that has mitred ends that are parallel to each other needs to be cut longer to accommodate the thickness of the material you’re using. In this example, the single-unit side with parallel mitres measures 10 5/8" long (10" + 5/8") and the two-unit side is 20 5/8" long. These longer pieces are shown in the plans, but it’s easy to forget and cut them too short. Double-check before cutting.

A Representative

Since all of the shapes are made in much the same way, I’m going to use an L-shaped piece as the representative for how to build the pieces. Simply apply the same method and order of operation to build the rest of the tetrominoes.
The L-shape assembly is made of seven pieces: one piece for the back panel and six for the sides. As mentioned earlier, two pieces have mitres parallel to each other, so be sure to add the 5/8" of length when you’re making these parts.

At your tablesaw, cut the four pieces that will have non-parallel mitres to length: one piece 30" long, one piece 20" long and two pieces 10" long. Next, cut the two pieces that will have parallel mitres: one at 20 5/8" and another at 10 5/8".

If you are using material that is the same on both the front and back edges (standard, square-edge MDF, for example), the layout is very easy because you can flip the parts over for assembly. However, if you are using material with a factory-finished or profiled edge—such as the bullnose MDF I used—you will have to keep in mind which edge faces forward as you cut your mitres. It is easy to end up with a piece that is cut “backwards” for your shape.
With the sides cut, arrange them on your bench to form the L, and then use a pencil to mark the location and direction of your mitres. This step may seem unnecessary, but trust me—it’ll save you a lot of frustration, mistaken cuts and wasted material.

Mighty Mitres

The mitres have to be perfect for this project. The easiest and safest way to cut them is with a cross-cutting sled on your tablesaw. Tilt your blade to exactly 45° and use a sharp cross-cut or combination blade to cut the mitres. Since all the pieces were cut to length in the previous step, be careful not to shorten the overall length as you prepare their mitres. You may need to make multiple passes and “sneak up” on the perfect cut.

Once you have all ends cut to the correct mitres, reassemble the L shape on your bench with the front edges facing down. Hold everything together temporarily with masking tape only—no glue just yet. Next, mark the inside edges where the rabbets to accept the back panel will be cut. Just like when you marked the mitres, this extra step marking the workpieces will save frustration later, especially when you make more complex shapes, such as the stubby-T assemblies. It’s very easy to cut the rabbet on the wrong edge.

Rabbet Runs

You need to cut the rabbets 1/8" wide and 3/8" deep into the MDF sides to accept the back panel. How you cut these is up to you—you can use a table-mounted router spinning a straight bit raised to 1/8" above the table; you can use a dado blade in your tablesaw; or you can do as I did: I used a full kerf (1/8" thick) tablesaw blade raised 3/8" above my tablesaw and ran the workpieces on edge over the blade using a tall auxiliary fence for support.

Assembly

To assemble each tetromino, I used wood glue applied to the mitred edges, then reinforced each joint with a couple of 23-gauge pins per joint. Apply a good layer of glue to both mitred edges and bring your pieces together. I “clamped” the corners together using a few strips of masking tape, then added the pins. If you are using prefinished workpieces, as I did, wipe away any glue squeeze-out with a wet rag right away. If you are using solid wood or veneer, wait until the glue has hardened partially and remove it with a sharp chisel to avoid finishing problems later.

Finally, use a small square to be absolutely sure all of your corners are 90°, shifting the assembly as needed until all of the corners are perfect. Measuring and equalizing diagonals across the square and rectangle sub-shapes is a fast way to make the assembly square. Give the glue an hour or so to set fully before moving anything.

Back it up

The easiest way to make a back panel for a tetromino is to lay your assembled shape on a sheet of white hardboard and mark the location of the inside edges of each shape right on the board with a pencil. Once you remove the tetromino, you simply draw a second line 3/8" out from the first traced line, to account for the depth of the rabbets (3/8") in the back edges of the sides. With the back panel traced out, cut the shape using a bandsaw or a jigsaw. Test-fit the back panel into the assembled tetromino and make any adjustments required for a reasonable fit.

Before you attach the back panel to the sides, you should paint the back piece. A word on colours: after an hour of searching online for the proper colours to match my pieces with the Tetris game pieces, I realized that there is really no consistent colour-to-shape relationship. In the end, I just selected seven colours of gloss Krylon indoor/outdoor spray paint that were close to the colours in a couple of pictures I’d seen. In short, there is no “proper” choice when choosing your colours; just go with what pleases your eye. In my project, the colours shown are Sun Yellow, Regal Blue, Emerald Green, Blue Ocean Breeze, Bauhaus Gold and the (surprisingly) simply named Purple.

When the paint is dry, all that is left to do is to insert the back panel and lock it in place by driving a 1/2"-long brad nail every 2" around the perimeter of the hardboard and into the MDF sides. This step can be done with finishing nails and a hammer; but if you have an 18- or 23-gauge nailer (or were looking for an excuse to buy one), it makes the job much faster and easier. Touching up the nail holes was very easy with this project. Rather than the traditional wood-filler approach, I decided to try a painter’s touchup pencil instead. These crayon-like pencils are used to fill nail holes in prepainted trim and just happen to work great for the holes in my prepainted MDF as well. No touchup pens available? Try a crayon. I borrowed one from my daughter, just to make sure it works. While it is a bit messier than a proper filler pencil, it still works great.

That’s it. Inexpensive materials, relatively simple construction techniques and a weekend in the shop all came together to make a great-looking addition to a child’s room. If you are going to arrange a tall, vertical shelf, make sure you secure the pieces to keep little ones safe. The only hard part comes when you stack the shelves. You will have to persuade yourself that the shelves don’t need to be re-stacked (for the fifth time!). Just like the video game, putting these pieces together can become a little addictive.

Putting up the shelves an be a puzzle unto itself. Keep this image handy as a guide.