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This is a very simple pattern to cut. It is all 1/2" thick wood and there are only four interior cuts. You can cut this from hardwood, plywood. If you use MDF then a paint job is probably needed.
There is a lock pin to hold the halves together. This seems cruel but no dogs were harmed in the making of this project.
I used a 1/4" diameter wooden dowel and cut a slot in the end to hold a thin wedge. I cut the wedge on the scroll saw. It holds pretty well
I did not cut the cat version but you can see the included parts in this image.