Summary
This 4x4x4 version of 3D Tic Tac Toe is what I grew up with: I like it much better than some of the 3x3x3 versions you see because this almost never ends in a draw. The strategy is actually pretty involved. 3D printed, 3D Tic Tac Toe?... why not? The Xs and Os are the same piece designs from what I've had on Shapeways previously: I'm uploading the piece designs here, along with an improved stand design.
The improved stand (see renders) can be printed as 4 separate units which stack one atop the other. It's better than the original one (pictured) because 1) it means you can partially disassemble the stand to access some of the middle spaces if you need to, 2) pieces could fall through the old grid design, and 3) although the double helix supports are kinda neat, it made the whole thing quite springy which is not a great quality in a stand.
I hope you like it, and invite you to check out some of my newer designs on my Shapeways store (I put them up at shapeways.com/shops/mikelepage first, then may move them here later if there's enough interest).
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