Impossible Marble in Truncated Cube




Introduction: Impossible Marble in Truncated Cube

This project was inspired by a youtube video. I came up with the shape and the method to cut and stain it. This turned out to involve more interesting math and woodworking problems than I had expected!

If you want to make one yourself, you will need:
  • Wood (preferably a soft wood like pine)
  • A nice marble
  • Woodworking machinery (drill press, table saw, bandsaw)
  • A good vice
  • A way to boil water
  • Optionally, sanding and finishing supplies

Step 1: Cut a Cube and Drill Holes

Cut yourself a cube. I did this with a table saw sled and a stopper block. Once you have the distance you want set, you can simply rotate the wood around until you've cut it down to the right size on all three axes.

For the holes you'll again want to set up some stopper blocks. Find the center of one side of the cube and center it perfectly under your drill press, then fix two pieces of wood to form a corner that you can true it up against. Now drill through from all sides. It might be best to go through each side rather than through the entire cube in order to minimize any tear-out.

The big question here is what size the drill bit should be. There's some fun geometry involved that you can read about in my blog entry about this project here, but all you really need to know is that the drill needs to be at least 71%, or [1/sqrt(2)] the diameter of the marble. This is the size ratio at which the marble will be touching the corners of the intersecting tubes. If you want your marble to rattle around a bit, try something like 80-90% of the marble's diameter. I went with 73% because I didn't have any bigger drill bits on hand. My marble can be rotated, but doesn't rattle.

Step 2: [Optional] Truncate the Cube

You can finish the cube however you'd like - round the edges, cut some chamfers, etc. I didn't want to break out the router so I decided to try truncating the cube. This turned out to be quite tricky, but I managed it in the end.

I first marked the cut lines by creating an octagonal template the size of the cube's sides and tracing it on each face. I then made a sled to secure the cube at a 45 degree angle from the table. Setting the cube in this sled brings four of its corners into the appropriate vertical plane needed for cutting them off with a bandsaw. Once everything was in place, I just freehand cut along the template lines, rotating the cube to bring each corner into position.

Some quick sanding, and we have the final shape!

Step 3: Boil the Cube

There seem to be several different methodologies for this sort of thing. Some people submerge the wood for a day or more, in cold or hot water. I prefer the faster method of microwaving. I simply put the cube into a mug, covered with water and held down with a rock (you probably shouldn't microwave rocks, but that's all I had on hand. Rocks may explode in the microwave if they contain moisture. Try wedging another piece of wood in to hold it down or something). I then microwaved it until the water was boiling, and boiled for something like three 30-second sessions. The water boiled over aggressively around the wood. Just refill if you lose too much.

I don't have a picture of the actual boiling, but you can see the resulting 'tea' and the rock I used as a weight.

Step 4: Quick, Press It In!

Okay, so you should have done some prep work before boiling the wood. I'm just going to assume you're not following this step-by-step without reading through the whole thing first.

Open your vice large enough to fit the cube, some padding, and another scrap piece of wood as a press block. Drill a hole partway into that scrap piece to hold the marble in place. Once the wood is done being boiled, you'll run over to the vice and secure the wood between the padding (I just used a paper towel) and the presser block, with the marble sandwiched in between. The youtube video that inspired this suggested coating the marble in oil, but I didn't do that and it didn't appear to be necessary.

Make sure that you are pressing the marble through a hole on the END GRAIN side of the cube. This will minimize the chances of your cube splitting from the stress.

Carefully apply pressure with the vice until the marble goes into the cube! My marble wasn't entirely in yet when the cube and press block made contact, so I had to remove the cube from the vice and press the marble the rest of the way in with a nearby socket wrench. You'll probably want to have something like that nearby in case the same thing happens to you, or engineer some better way of pressing the marble with the vice. The youtube guy used a piece of PVC instead of a presser block. If you can find a hard tube small enough to fit through the drill holes, that would be perfect.

Step 5: Dry and Sand

You'll want to let the wood dry for a few days afterwards. Try to let it dry slowly to minimize chances of cracking - don't speed up the process with a fan or a heat gun or anything.

The wood will have a little bit of a disheveled appearance after the boiling, even if it was smooth to begin with. You can just sand it down and then finish it like any other piece of wood once it's dry. If you want to sand the inside edges to loosen the marble a bit or tidy up, you can floss a thin strip of sandpaper in through there to remove material. I was able to get my marble to rattle a bit with this method. I also wrapped the end of a steel rod in a sandpaper strip and used that to smooth the insides of the holes a bit.

Step 6: [Addendum] Stain and Finish

I'm adding this extra step to the instructable after writing up the rest of it yesterday because today my piece was dry enough to sand and stain. Rather than give you instructions, I'm asking for some advice!

I went with a dark walnut stain as several recommended, and I like the way it looks with the color of the marble and how it brings out the grain a bit. The problem is, I'm not sure how to deal with the holes! For now, I've simply gone around them carefully and left them completely untreated. I'm okay with this look, but I think it would be a bit nicer to have them stained as well.

*Edit 2*

I solved the problem! My solution was to use plastic wrap to envelop the marble and protect it from the stain. It was tough to get into position, but once there it worked like a charm!

When you try to get the wrap to go all of the way around the marble, it tends to bind to itself and possibly tear. The method that finally worked for me was as follows: cut a square of plastic wrap (maybe 5" to a side) and twist/roll all four corners. Now you should have a flat section with four sturdy little 'ropes'. Choose a hole and insert these ropes one-by-one, bringing them out of each of the four adjacent holes. You can use tweezers to help pull them through. There is a photo of this step above.

You can then thread the ropes back through their holes and out of the bottom one. Now you have all four coming out of one hole (the opposite of the one you originally inserted them into), and you can pull on them and fiddle with tweezers until the flat part of the plastic wrap is totally protecting the marble. Twist the ropes together into one strand and you've captured your marble!

Now you can just use a paintbrush or Q-tip to daub stain inside of each of the holes. Wait until it's thoroughly dry to pull the plastic out! All of the wood should now be nicely stained, with the marble remaining flawless.

Enjoy your new conversation-starter/desk toy! I find that the shape is quite fun to fiddle with. Thanks for reading, and be sure to send me pictures if you make one yourself!

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71 Discussions

How would you get the walking stick inside the cube?

Well, I was thinking it would be the top of it, sort of a Shamanic rain stick type thing...

Awesome and I just suggested to my son that this would be a great class woodshop project. Project using math skills ='s too awesome! Thank you.

to help with the cracking problem, let the cube dry in a paper bag. I know it sound weird and I don't know why it works, but it does (usually)

I just did a bunch of these as a little project with a couple of 5 and 12 year old girls.

I used pine cut from a 2x4, microwaved the wood blocks individually in a teacup with a half-cup of water and a little plate over it for 1+1 minutes, and used a hand clamp to force the marble in. To push it all the way in (not just flush), I found it easiest to use a socket fitting over the marble as I clamped it. I let them dry for a while, sanded them, and then the girls painted them and extras with the marble outside (to show the challenge) with watercolors that let the wood grain show through. Total time less than 3 hours! A very nice science/art project....

The 12 year old gets the science, the 5 year old mostly liked painting it. ;-)

1 reply

Those are awesome! That makes me really happy to see, thanks so much for sharing. I look forward to doing these sorts of things with kids when I become an uncle/father myself.

They can print a wood fiber/plastic composite rather like sawdust with a PLA binder. You can even tone it (e.g., to create a fake woodgrain) by tweaking the temperature during printing to lightly brown the wood. PLA is such a great material to print that I've not been tempted to try the fake wood....

Ok, I've done one, what do you think?

Marble 14.8mm, holes 12mm, mahogany (or similar)
Steamed in a vegetable steamer, in the steam, not in the water. I did a test piece for an hour, it went through so easily with a lever press I made and a small socket, so I just heated this one 45mins. I don't think the point is to cook the wood, only to make sure it is heated through, so my next one might be just 15 mins. Finished with a little fine sanding and rubbed in some wax polish. Very happy to have another home-made curiosity, thanks for the idea!

Marble in cube.jpg
2 replies

That is absolutely beautiful! I love the way the edges of the holes are smoothed. How loose is the marble with that ratio? Thanks for sharing!

Glad you like it! The edges of the holes were going to be chamfered but on the first one my lousy drill chattered, so I sanded them by hand (thumb) and gave them a more rounded edge. The marble can move about 2mm each way so it rattles a bit, and you can tell it really is a marble and see it is impossibly trapped. I'll see if I can find out how to vote for you.....

Hey congratulations on being a finalist in the weekend projects contest! I really love this. Not only do I want to make one (I'm hunting for a really wicked marble) but I am going to see if we can't do this as a project for the boys next year at the camp I work for. Good luck and again gratz!

1 reply

Oh wow, thanks! I hadn't realized that I was a finalist. I'm glad so many have enjoyed my instructable. It's really wonderful to think that I'll have helped/inspired people to have fun with woodworking. Good luck finding that marble!

Stain it before you boil it 3 or 4 good coats of stain will hold up to a boiling then your stained all the way through ! make sure you let the stain dry completely before boiling !