Woodworking Geometry Lab
Model the angles. Visualize the cuts. Design with confidence.
Tapered Polygon Box
Design and generate a complete build plan for a tapered polygon box using your table saw and sled. Enter the number of sides, top width, height, and taper angle to model the geometry, calculate the required blade and fence settings, and visualize each cut before you make it.
All inputs are interconnected — adjusting one value influences the others. Start with your overall form (side count, width, height, taper), then refine until the proportions and angles feel right.
Understanding the Geometry
The Number of Sides determines the overall shape of the top and bottom polygons. The Side Piece Miter Angle controls how those pieces meet around the ring. Together, they define the Joined Edge Bevel Angle — the precise bevel required so each side closes cleanly into a tight, gap-free form.
Because the bottom polygon is smaller than the top, the box naturally tapers inward. That difference creates the Box Taper Angle. To keep the finished piece sitting flat and symmetrical, the top and bottom edges of each side must be beveled to match that taper.
How the Inputs Interact
These dimensions are mathematically linked. Changing one value will often recalculate others to preserve a valid geometric shape.
- Changing Width of Sides at Top or Width of Sides at Bottom recalculates Side Piece Miter Angle and Box Taper Angle to maintain proper geometry.
- Changing Side Piece Miter Angle recalculates Box Taper Angle and Width of Sides at Bottom (Width of Sides at Top remains fixed).
- Changing Box Taper Angle recalculates Side Piece Miter Angle and Width of Sides at Bottom (Width of Sides at Top remains fixed).
- Changing Box Height recalculates Side Piece Height and Width of Sides at Bottom (Side Piece Miter Angle remains fixed).
- Changing Side Piece Height recalculates Box Height and Width of Sides at Bottom (Side Piece Miter Angle remains fixed).
- Changing Number of Sides recalculates Side Piece Miter Angle and Width of Sides at Bottom (Box Taper Angle remains fixed).
Built With This Geometry
These pieces were designed using this geometry model and built with standard table saw setups.
Min: 4 / Max: 20
Min: 1 / Max: 50
Min: 0 / Max: 50
Min: 1 / Max: 72
Min: 1 / Max: 72
Min: 0 / Max: 59
Min: 0 / Max: 59
Min: 0 / Max: 8