Introduction: Caged Tetrahedron Puzzle

Picture of Caged Tetrahedron Puzzle

This puzzle will test your spatial ability. The goal is to remove the tetrahedron (triangular pyramid) from the cage. It's really pretty straight forward if you paid attention in geometry. So, can you figure it out from the pictures shown in Step 11? If not, refer to this video.

Note that this is a modification of a puzzle I saw online*. That version looks pretty nice and runs about $21 with shipping.

*Amazon Affiliate Link

Step 1: Tools/Materials

Tools

  • Table saw
  • Jig Saw (optional)
  • Drill press
  • Center punch
  • Forstner bit (3/8")
  • Wood clamps
  • Ruler
  • Pencil
  • Sander

Materials

  • Wood: 10" x 4.5" x 1/2" thick
  • Wood: 2.5" x 2.5" x 2.5"
  • Dowel, 3/8" diameter x 36" long
  • Glue
  • Paint / Stain (optional)

Step 2: Tetrahedron

Picture of Tetrahedron

Ok, I still consider myself an amateur woodworker at best so I didn't want to try to make the tetrahedron shape. Therefore, I took the easy route and 3D printed this part. I pocketed it out to save weight (cost) but this also made it easier to grab and manipulate which took away a little bit of the puzzle challenge (not a good thing). I've provided dimensions for a solid version that hopefully a woodworker with more talent than me can produce :).

Note that the tetrahedron size is arbitrary. However, you must size the cage opening to get the correct fit. You can either work the geometry (Pythagorean Theorem) by hand or refer to table for other sizes. For the table, the tetra size (L) for this build is 2.5". This requires a square opening on the top of 1.768" (L/2^0.5). I added 0.025" to this dimension under the "recommended box opening" column to guarantee fit.

Note that the exact dimensions shown for the tetrahedron are slightly too big for my cage opening (Step 5). You have a few options:

  1. Round the edges/points of the tetrahedron by ~ .010"
  2. Increase the cage opening (hypotenuse) to ~ 2.55" (Step 5)
  3. Reduce the tetra sides down to 2.4"

My 3D print came in small so I was good. If I made it from wood, rounding the edges would have been the optimum choice for me. Note that with use, the vertices will get rounded very quickly anyway.

Step 3: Cage

Picture of Cage

This cage is designed for the 2.5"/side tetrahedron shown above. You will building to this drawing. The parts are color coded for easy reference.

Step 4: Base

Picture of Base

This part is straightforward. Use a saw to cut to the dimensions shown. Mark the hole locations with a pencil and drill holes. I used a 3/8" Forstner bit and drilled from both sides for cleaner holes.

This video has nothing to do with the project - just me playing with a slow motion while drilling a hole.

Step 5: Top - Option 1

Picture of Top - Option 1

You have two options here. This step is showing the first option. The overall size is the same as the bottom. However, as you can see, the center section is cut out. For this cut, I would drill a hole in the center and use a jig saw to remove the middle section.

Step 6: Top - Option 2

Picture of Top - Option 2

This seemed like the easier approach for me. I cut individual pieces and glued them together. Refer to the previous step for detailed hole dimensions.

Step 7: Cage Bars

Picture of Cage Bars

The bars of the cage are made from 3/8" diameter dowels. Cut eight pieces to the dimensions shown.

Step 8: Match Drilling

Picture of Match Drilling

You could either mark and drill the top/bottom separately or match drill. To me, match drilling was an easier way to guarantee hole alignment. Recall that the bottom holes were drilled in Step 4. Tape the top and bottom bottom pieces together. Using the bottom piece for alignment, use a 3/8" diameter Forstner bit to drill 1/2 the way through the top. Make sure to add a small mark to the sides so you will be able to match orientation later.

Step 9: Assemble Cage

Picture of Assemble Cage

Add a small amount of glue inside the holes. Place the dowels in the holes as shown. Getting all eight dowels to line up was a little challenging. I had to ask one of my kids for help (extra set of hands) on this step.

Step 10: Clean Up & Finish

Picture of Clean Up & Finish

Sand to break sharp edges and clean up the dowel locations. At this point, you can paint or stain as desired. I used a black cherry stain with 2 coats of polyurethane.

Step 11: Pictures

Picture of Pictures

Here are a few pictures of the completed puzzle. As for puzzle difficulty, I would rate this on the easier end compared to some of my others. Most people should be able to figure it out within a few minutes.

Step 12: Suggested Changes

Picture of Suggested Changes

After building it and seeing the proportions, I feel the tetrahedron should have been larger in comparison to the cage. I also think the height of the cage should be reduced. I've included new dimensions for all the parts in this step. Although not shown, another change would be to add in another dowel per side. This would limit access and therefore make it more of a challenge to remove the tetra from the cage.

Step 13: Fully 3D Printable Version

Picture of Fully 3D Printable Version

The green version was printed 1:1. The purple version was scaled 50% larger. Note that I used a low end 3D printer for these parts which didn't hold the dimensions very well. With that, I needed to sand down the opening in the purple version by ~ 0.03" to allow the tetra to fit inside. If this happens to you, I suggest reprinting the tetra at a slightly smaller scale.

Thanks for viewing!

Comments

skitcher1101 (author)2017-11-21

3d printed one plz

mtairymd (author)skitcher11012017-11-22

Just added the files...see last step :)

skitcher1101 (author)mtairymd2017-11-22

Thx! Printing one soon. I figured out the solution before watching the videos or making one :)

random_builder (author)2017-11-21

This is awesome! I think it is your best one yet!

pjotrkuh (author)2017-11-21

Nice! You could probably use a D&D d4 dice too!

mtairymd (author)pjotrkuh2017-11-21

Ok, I had to look up D&D d4 dice. Yep, that would work!

boesh (author)2017-11-21

Hahahaha slow motion video test ... great !

mtairymd (author)boesh2017-11-21

Yep, I was bored :). Now I really want a camera that can shoot more than 60 FPS.

tomatoskins (author)2017-11-21

I've had this puzzle on my mind for a couple months now, and you beat me to it! :) Amazing job! I always love your puzzles!

mtairymd (author)tomatoskins2017-11-21

Thanks. You and I think a like! I was going to make the ball in the cube and the next day I saw you posted a much nicer version than I was thinking about.

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Bio: I like to design and build random things.
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