You don't need a laser cutter to make this project - it just makes it a lot faster. I used the one at TechShop. It's easy to turn your own 3D model (whether you designed it or found it on 123D as I did), scale it to any size you want, and print out the plans for it. 123D Make even provides directions for how to put it all together.
Step 1: Using 123D Make
If you want to play with the model that I made, check it out here: http://www.123dapp.com/3dmk-Make/Giant-Cat/656520
You can see in the second image that the tool bar on the left allows you to do all of these things, including change the direction of the slice and change the form somewhat.
On the right hand side, it shows you what cuts it plans to make based on the size of your model and direction of your slice. After inputting the size of the cardboard I had on hand, it compiled a tidy little file of all the cuts for me which I then downloaded.
The third image shows you the order for putting your pieces together in a neat little slideshow, and highlights which piece is coming up next. Seems unnecessary until you have tons of pieces in front of you that seem to make no sense whatsoever. It happens.
If you don't want to play with the model here, and just want to make it, I provided the .eps files for you to download here!
Step 2: Assembling the cat
If you've decided to cut these out by hand, I strongly suggest numbering each of the pieces using this same system. Until I figured that out, I had a really hard time figuring out the orientation for the smaller pieces.
Then it's just a matter of gluing everything together. I used Quick-Dry Tacky Glue, and it was amazing! Super-fast tack and a really nice finished bond.
I kept the 123D app near me to help walk me through the more confusing parts of construction. All in all, I think it took me less than 2hrs to glue each of the 170 pieces together, which was considerably less than I had anticipated!
Step 3: Introduce kittens to their new friend
Eventually the kittens got down to business and determined their dominance over the new cat. It wouldn't even fight back! But even cardboard cats are interested in hunting pigeons, so in the end they found common ground and settled into their new life together.