How to Make 2-D Dome Segments

Calculate length A by multiplying the desired radius of your dome by 0.61803. Calculate length B by multiplying the radius by 0.54653. Record these lengths for reference.

Construct an equilateral triangle. Open your compass to length A and use it to draw a curve that would cover about one-third of a circle. The point where you place the compass spike is the first corner of the triangle. Pick a point near one end of the curve to serve as a second corner. Place the spike at the second corner and draw a short curve intersecting the first curve. The intersection is the third corner. Connect the three corners and draw glue tabs 1 cm wide along each side of the triangle.

Construct an isosceles triangle by opening your compass to length B and drawing a curve, marking the spike's location as the first corner. Extend the compass to length A and place the spike at one end of the curve, then draw a second short curve that intersects the first curve. The location of the spike and the point of intersection are the second and third corners of the triangle. Connect the corners and draw glue tabs 1 cm wide along each side of the triangle.

Continue constructing triangles with tabs until you have 10 equilateral triangles whose sides equal length A and 30 isosceles triangles with two sides B and one side A. (The lengths A and B exclude the glue tabs.)

Cut out the shapes and fold back the glue tabs. You now have enough segments to create a geodesic dome.