Rugs, Carpets and Carpeting - DIY Chair mat from plywood and carpet tiles

I've got new plush carpet on a concrete slab in the basement. I've also got two computer desks with rolling chairs. I've tried several clear plastic chair mats to protect the carpet and allow the chairs to roll. They work, but eventually they crack, and the plastic is cold on bare feet. Besides, I don't like the look of these plastic mats, and I can never find the right size to fit the desks well.

I had an idea of cutting a custom shaped floor "mat" out of a 4x8 sheet of plywood, and then applying carpet tiles to that to make a foot-friendly and fashionable chair mat. I'm not sure how thick the plywood should be. I'm hoping to use 1/2 inch. And I'm not sure how to handle the edges to avoid splinters.
Can I just bevel the edge and wrap a couple inches of carpet tile around to the bottom of the plywood?

Any thoughts on this idea? Alternatives? I like playing with colors, and have already found several carpet tiles that would look well as a chair mat. I know the carpet tiles would be durable, but I'm not sure how the plywood would hold up.

Your problem is not the carpet, it's the pad under the carpet. I've installed many "office" areas like that in folks homes and it works well. I strip and pad every place except where the chair is going to be rolling around. This area gets no pad and is bordered with tack strip. When I stretch in the carpet, I'll staple the carpet to the lower edge of the strip and then let the rest of the carpet just lay on the bare floor with no pad under it. Unless someone is looking closely, it isn't readily obvious and yet provides an unpadded area that is easy to roll a chair around on. If you don't want to tackle this on your own, you could hire an installer to remove the pad in that area and re-install the carpet accordingly.