The oak trim would add to the thickness of the joints doubling the glue
area and providing adequate strength. The oak would also dress up the box
and contrast nicely with the hunter green paint I chose for the plywood.
The box dimensions, determined somewhat by the material I had on hand, is about 10 x 11-1/2 x 15-1/2 inches. It is six-sided so the plywood requirements are:
10 x 11-1/2 inches, 2 pieces
10 x 15-1/2 inches, 2 pieces
11-1/2 x 15-1/2 inches, 2 pieces
There are four oak strips for each side. I cut 3/4 inch thick
oak into 1-3/8ths inch wide strips and then resawed those on the table saw
to about 5/16ths inch thickness. I stacked the strips and mitered the ends
at a 45 degree angle, eight at a time. The oak requirements are: 1-3/8 x 10 inches, 8 pieces
1-3/8 x 11-1/2 inches, 8 pieces
1-3/8 x 15-1/2 inches, 8 pieces
I glued the oak strips along the edges of the prepainted
plywood panels and held them in place with clamps and 5/8ths inch long
staples from a pneumatic staple gun. I tried to keep the staples far
enough away from the edge to avoid the saw blade when the edges were later
bevelled. The pneumatic gun set the staples a little too deep below the
surface resulting in protrusion on the other side. By holding the gun at
an angle I was able to keep them from being set so deep and going all the
way through.
I tilted the table saw blade to 45 degrees and bevelled the edges of
the six panels. There are four final passes to be made at each of the
three major dimensions. It is more important to have square corners, good
clean bevels and consistent dimensions than it is try to maintain a
predetermined dimension so try to make all cuts of each dimension with
only one change of your table saw fence. 
I applied yellow glue liberally to all bevelled edges of the box and
assembled it using twine to hold it together. I wrapped two sets of two
turns each around each major dimension and tied each set with a square
knot. Then I gradually tightened each wrap by inserting a short stick
between the twine and twisted in a kind of Spanish windlass. Where
necessary to even out the tension I inserted sticks and twisted on the
opposite side of the box. This is where accuracy of the cuts is important
because that is what determines the squareness of the joints. 
I picked
one side of the box to be the top and set the table saw fence to 3 inches.
I set the blade height to cut through the side laying against the table. I
cut three sides around the top then before cutting the fourth side I
inserted 1/8th inch material equal to the saw blade thickness into the
kerf, clamped it and proceded to cut the remaining side. 
I screwed a pair of
hinges to the back of the box and found that the oak trim required some
clearance to allow the top to open. The belt sander bevelled the ends of
the trim as shown in the picture despite some interference from one of the
residents of the shop. The box may be used for tools or perhaps as a
coffin for a small animal. 
This project
served as practice and a learning exercise for some cabinets I plan to
build in the future. Next time I will try to glue the trim pieces together
into rectangular frames that can then be glued to the plywood panels. That
should minimize the need for staples to hold the trim in place and provide
tighter joints between the ends of the trim. Thormon Ellison
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