Math CentralQuandaries & Queries


Question from Corey:
I'd like to build an octagonal poker table using 4'x8' sheets of plywood.
I would like each side edge to be approx. 2' wide.
I am sure that due to the angles I can do this with one sheet of plywood,
but i don't know how to measure for this.


There are various possibilities. If you have a plywood with a nice, very straight, grain parallel to one side, and you don't plan to cover it, you could consider cutting seven triangles and two half-triangles as shown

first pattern

and assembling them points-in over an appropriate frame; the grain will give a lovely octagonal pattern.

pattern 1 assembled

However the joinery in the frame below will be tricky. This might be better as a veneer pattern!

If you want a simple design for the frame underneath you want to keep the cuts few and symmetric. About the simplest would be in the diagram below.

second pattern

This will also show off a strong but wavy grain (like most oak-surfaced plywood,in which the face veneer is rotary-cut) better than the pattern above will.

Note that the diagonal edges in the middle are each more than an inch away from the center. If you wish to use tongue-and-groove or some other routed edge pattern to make a strong permanent joint, you can easily push the top piece down and/or the bottom piece up to give a little extra wood along the long edge for jointing.

On the other hand, if storage is a problem, this design would work well for a tabletop that disassembles into two halves, with folding legs and an unglued lap joint.

Good luck!

Corey wrote back

This is perfect, but I have one more question. How can you insure that the angles are all identical so that the octagon is symmetrical?


If you are making RD's first design then I wouldn't measure angles at all. Mark 2 foot measurements down one side of the sheet and then on the other side 1 foot, 3 measurements of 2 feet and the 1 foot. Join the markings as in the diagram and cut along the lines.

If you are looking at RD's second design then the angle between the 4 feet 9 and 3/4 inch sides and each 1 foot sides is 90 degrees. All the other interior angles are 45 degrees.


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