I'm trying to make a wooden pyramid, preferably triangle based, but from what I can find square would be easier, with a specific sized face.

I wanted the faces isosceles triangles with 3 7/8 in bases, 4 1/4 in tall, with base angles working out to be 65.5 degrees - the angles are important, the lengths can stand to be varied.

I went ahead and made a mock up, but the 30 degree edge cuts left me with an odd sort of 3d kite instead of a pyramid.

So how can design a pyramid with a specific face size, either triangle or square based.

I believe this is a basic carpentry question that I have dealt with on numerous occasions. I have attached a sketch so you can follow along. This method works for any geometric figure with an equilateral base; pyramid, pentagon, hexagon, whatever. The trick is to build from the inside out, not outside in. (This can also be done with non-equilateral figures but requires separate members for each angle.)

1) Draw the base, either full size or scaled. 2) Draw lines bisecting each corner, perpendicular to the opposite side. 3) Measure the length of any one of the lines from the corner to the point where the lines intersect. This will be the length of the base of a right triangle. 4) Using the height you have established (4.25") and the length of the base, with the Pythagorean theorem, solve the length of side c on the right triangle. 5) Construct 3 right triangles with these dimensions and join them at side b on the base you have drawn. 6) It is now just a matter of paneling each face of the figure and you will have a pyramid, or whatever geometric figure you are building.

I have constructed several of these with tongue depressors, in the past, to teach some of my apprentice carpenters how to do it. Its actually quite easy to do.

I just noticed you want the figure to be hollow, so just build a scaffold using the method described above. Make the scaffold from heavy cardboard, edge glue the panels over the scaffold and when the glue has cured, remove the scaffold.

I just cut out two sides out of some scrap to get my head around how they would be put together, the final will be using a much thinner wood to leave space on the inside.

If it was me, I'd have to guess, try, reguess, try again, sand, glue and putty the heck out of what was left.

Good luck.

1) Draw the base, either full size or scaled.

2) Draw lines bisecting each corner, perpendicular to the opposite side.

3) Measure the length of any one of the lines from the corner to the point where the lines intersect. This will be the length of the base of a right triangle.

4) Using the height you have established (4.25") and the length of the base, with the Pythagorean theorem, solve the length of side c on the right triangle.

5) Construct 3 right triangles with these dimensions and join them at side b on the base you have drawn.

6) It is now just a matter of paneling each face of the figure and you will have a pyramid, or whatever geometric figure you are building.

I have constructed several of these with tongue depressors, in the past, to teach some of my apprentice carpenters how to do it. Its actually quite easy to do.