Introduction: How to Build an Apollonian Gasket End Table

About: I am a Design Engineer student at Converse College who enjoys upcycling. While I don't have much experience building and refurbishing, I have a strong passion that pushes me to create good work.

An Apollonian Gasket is a fractal generated by using tangent circles to fill an area. The circles decrease in size and can become infinitely small if the fractal is continued. The table uses increasing numbers of circles in each layer to create an end table with various depths. It was inspired by my current math research on Apollonian Networks and designed with consideration of my senior capstone project on automotive furniture.


All of the materials I used were scraps. The table can be made with various thicknesses of wood, however, dimensions may need to be changed if you do so. The materials I used were:

  • Titebond Premium Wood Glue
  • 120/180 Grit Sandblock
  • 9/16" Spade Drill Bit
  • 1 1/2" Hole Saw Bit
  • Dewalt Drill
  • Bandsaw
  • Spindle Sander
  • Table Sander
  • Sandpaper
  • Clamps
  • Scrap wood (large sheets and 1"x1" poles)
  • Black Spray Paint

Step 1: Design Apollonian Gasket

I designed my Apollonian Gasket in Revit, however, you can use this link to design one without needing math. The outer edge normally is circular but I used a decagon for leg placement reasons. To design in Revit continue with the steps below.

  1. Draw an inscribed polygon extrusion with 10 sides, an 8" distance, and 1/4" depth (Don't worry if your wood is not this thick it won't matter for the design)
  2. Draw the circle void extrusions with a 1/4" depth. The diameters are given below from largest to smallest. Each circle should approximately 1/4" away from any other circle. The positioning of the circles correlates to the apollonian gasket provided.
    1. Circles #2 have a 7 1/4" diameter. The circles should be 1/8" away from the center of the decagon and 9/32" from the edge of the decagon.
    2. Circles #3 have a 4 3/4" diameter.
    3. Circles #6 have a 2 1/4" diameter.
    4. Circles #11 have a 1 1/8" diameter.
    5. Circles #14 have a 13/16" diameter.
    6. Circles #15 have a 3/4" diameter.
  3. Project the design onto a piece of craft paper at the scaled size and then trace it.
  4. Cut out the design including the void extrusions.

Step 2: Draw and Cut Layers of Table

Using the template created in step one, sketch out each layer with the correct holes.

  1. Circles #2
  2. Circles #2 and 3
  3. Circles #2, 3, and 6
  4. All circles

After the design has been drawn, cut each decagon out leaving some room on the edge for later sanding.

Step 3: Cut and Sand Gasket Holes

Use the 9/16" drill bit to create holes in the small circles on layer 4 and use the 1 1/2" drill bit to create holes in all of the other circles on each layer. When drilling the holes, try to drill near the center of each circle. Then, use the jigsaw to cut out the circles to the proper size. The smaller circles should not require the jigsaw as they are close enough to sand down to size. Lastly, use a spindle sander for fast and accurate sanding of each circle. Sand as close to the design line as possible without going past it.

Step 4: Glue Layers Together

Now that each layer is cut out and sanded, the tabletop can be glued together. Using any type of wood glue, apply a layer of glue to the side of layer one with the design sketched on it. Then, place layer two on top of layer one, design side up. Repeat this with layers 3 and 4 then clamp the 4 layers together. Use one camp at each corner of the decagon and at least one in the center. Allow to dry overnight or as long as your wood glue suggests.

Step 5: Sand Imperfections

With the tabletop in one piece, it is now time to sand away imperfections in the layers. I began with the edges and sanded them even on the table sander. Next, I sanded the two largest circles on the spindle sander. The rest of the circles were sanded down with a Dremel sander and sandpaper. When done all the circles should line up evenly with the other layers.

Step 6: Cutting the Legs

With the tabletop built, the next thing to do is make the legs. I began with 1" by 1" wood pole scraps and cut them into 19" long poles, you will need 10 poles in total. Then, make a mark at 16" and draw a line from the opposite corner to the mark (as seen in the pictures). This is roughly a 75-degree angle which I cut using a bandsaw. On the other side, cut a 5-degree angle with the longest side facing outward (see pictures for clarification).

Step 7: Making the Base

To make the base, another decagon will need to be cut out and sanded, however, no holes are required. Once the decagon is ready, apply glue to the 5-degree side of the pole and place it at any corner of the decagon with the 75-degree angle facing another corner. Then, nail or screw it in. If you find trouble keeping the legs in position while nailing try using clamps to hold it in place. Continue the legs alternating the way the 75-degree angle is facing and rotating around the decagon.

Step 8: Gluing Into One Piece

This set is easy, just glue the base to the tabletop. Pay extra attention to how the decagons line up and then clamp the two pieces together tightly. Let dry overnight or however long your wood glue recommends. After drying, sand down any rough edges.

Step 9: Spray Painting

While you can leave your end table the way it is, I have chosen to spray paint mine black. When spray painting, don't spray too close to the table and apply thin layers at a time. You'll want to go over it multiple times to get a true black color. Then, you're done! You have made a table.

Made with Math Contest

Runner Up in the
Made with Math Contest