# Building a finger-jointed polygon box

> a finger-jointed regular-polygon box, from triangle to dodecagon

Most boxes are rectangles. This one is not: it builds a regular polygon, anywhere from a three-sided triangle to a twelve-sided dodecagon, from a set of identical walls that each tab down into a slot in the base plate. Because every side is the same length and meets its neighbour at the same angle, the walls are interchangeable and the base does the alignment for you. Turn on the lid and you get a matching slotted top. The Assembled 3D tab shows the faceted box standing so you can judge the shape before you cut.

## What you need

- **Laser cutting:** 3 to 8 mm plywood or MDF. Measure the actual sheet thickness with calipers before setting the tool.
- **3D printing:** any rigid filament. 4 to 6 mm walls give the base slots enough strength.
- **Glue:** PVA wood glue and an elastic band that can wrap the whole polygon while it sets.
- **Finishing:** light sandpaper for the wall tabs and slot edges.

## Step 1 - Shape and size



**Sides** chooses the polygon, from 3 for a triangle up to 12 for a dodecagon. **Size** is the diameter across the shape, which sets how long each edge becomes, and **Height** is how tall the walls stand. **Thickness** must match your sheet, because every wall tab and base slot is derived from it.

## Step 2 - Walls and lid



- Every wall is identical, so the more sides you choose, the more copies of the same panel the layout produces.
- **Finger width** controls how wide each wall tab is. On short edges a smaller finger width keeps at least a couple of tabs per side.
- **Lid** adds a second slotted plate on top that the walls tab into, turning the open dish into a closed box.

## Step 3 - Check the assembly



Switch to the **Assembled 3D** tab and orbit the box to confirm the polygon reads the way you want and the walls are tall enough for the contents. The flat SVG view shows the base plate, every wall, and the lid if enabled, laid out for cutting.

## Laser cutting

### Before you cut



1. Measure your sheet with calipers and set **Thickness** to what you measured, so the wall tabs seat firmly in the base slots.
2. Run a test on the base plate and two walls first, and check the tabs drop into their slots with light pressure.
3. Cut the base slots before the outline where your software lets you, so the plate does not shift once free.

### Glue up



1. Stand each wall in its base slot, working around the polygon so the shape closes evenly.
2. Wrap an elastic band around all the walls to hold the angles while you glue the tabs into the base.
3. Fit the lid last if you enabled one, and leave it unglued so it stays removable.

## 3D Printing

### Slice and print



1. The 3D download is a zip with the base, every wall, and the lid if enabled, already extruded to the **Thickness** value.
2. Do not scale the parts in the slicer: it changes the tab and slot sizes together.
3. Lay each panel flat on the bed. The slots are already cut, so no supports are needed.
4. Print at 0.2 mm layers with 3 or more perimeters so the thin wall tabs hold.

## Make it yours

- Set sides to 6 for a classic hexagon planter or caddy, or push it to 12 for a near-round drum.
- Engrave a design on each identical wall before cutting so the pattern repeats around the box.
- Turn off the lid and shorten the height for an open polygon dish or coaster tray.

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Open the Angled Box Generator: https://www.mylasertools.com//angled-box-generator
Read online: https://www.mylasertools.com//learn/guides/angled-box-generator