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I have been making my own eyes for awhile now. I make them from liquid resin that I cast, and then paint them on the backs. I like doing this, because then my eyes are very unique to my puppets. These green eyes will be for the squirmy wormy puppet, and will match the color of the poof of hair on the top of his head and his nose.

 
Getting some more work done on the foxy lady puppet. Poured resin eyes, then painted them from the back. Made a pattern for the head pieces, then cut out and sewn. Made the nose out of sculpey clay, baked and painted. Still need to trim up some of the fur. I'll write more details later. -K
 
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Mouthplate with bottom thumb pocket sewn in.
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Nose pinned on to check for placement.
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Nose pinned on, holding eyes up to decide where they LOOK best.
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Puppet head after permanently attaching eyes and nose.
After finishing up the mouthgrip on the mouthplate inside the head, I get to turn it right side out again. I add the foam skull piece back in, in order to decide the placement of the nose and eyes. I can pin the nose on temporarily, then I can see where the eyes should go. This is a very important part of the puppet build, because the "focus" of the eyes needs to be just right. I want this puppet to appear to be almost peeking over his nose directly at the camera/audience. I used the seam as a guide to center the nose and the eyes, and decided on placing the eyes about 2 finger widths back from the top of the nose. This is going to differ from puppet to puppet. I really take my time getting the placement decided. I pin them where I think they should go- then I look at them straight on and from the sides. I also have other people look at them. (My kids are great critics!)
Before I sew the nose in place, I trim up some of the fur that will be directly under it (makes it lie flush to the head). After sewing the nose. I mark to small areas to cut just enough room to slide the posts from the eyes down into. I add the push-nuts onto the posts from the inside and they are locked in!
 
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There are many different things that you can use to build a puppet. A sock, a spoon, fleece, a box- the list goes on and on.
My monstery puppet will be built using a skeleton I construct from foam. The poly foam is 1" thick, and sold in rolls at craft stores for use in cushions and such things.  I just picked up a new roll today- I try to watch for 40% off coupons for my local craft stores. The glue I use is called Weldwood contact cement. 
I have built many different types of eyes. You can make them from styrofoam balls, ping pong balls, plastic spoons, ping pong balls and many other things.  The eyes I will be using for this puppet, I order from a supply store. *We'll talk more about the eyes when I am on that step :)
I end up hand sewing quite a bit of the puppet. I am pretty rough on thread, and found that a spool of upholstery thread works the best for me. It makes things sturdier, and if I need to use a lighter weight thread in some areas I can always do that.