This instructable details the making of a soft quilted tetrahedron costume for the more patient of my two cats.
Step 1: Choose fabrics and preprocess them
You'll also need an attractive color of quilt binding. Binding can be purchased at most fabric stores (I use Joanne's). The binding is a cloth strip that will sandwich the outer hem to create a finished edge. Also make sure you have a color of thread that matches your fabrics.
Step 2: Cut triangles and piece them together
Measure a strip of your 3rd contrasting fabric for the outside edge; the border shown in the pictures is a 2" strip. When the 4 triangles are sewn together and ironed into a bigger triangle, pin the border on the edge and sew in place. Once one edge is attached, cut the edges flush, iron flat, then repeat for the other edges.
Step 3: Attach batting and backing fabric
Place each pieced top right side up on top of the batting, making a batting sandwich, and pin it into place with basting pins (which are like safety pins, but shaped more conveniently for this purpose). Once the batting is pinned on, cut the sides of both the batting and backing fabric flush with the quilt top. It's easiest to use a rolling cutter and straight edge to do the trimming all at once.
Step 4: Attach binding, quilt along the color borders
Pin the binding strips to sandwich all three edges of each triangle. Fold the edge of the binding under at the corners to hide any unfinished edges. With your sewing machine set to very slow, carefully stitch the binding in place on all 9 edges. As you sew the binding you should aim your stitches at the very edge, no more than a millimeter from where the binding meets the quilt top.
I also chose to quilt another line a quarter inch out from the binding seam. This gave it a nice visual border and took care of holding the binding on at any of the points where I messed up on the initial seam. Specifically, it's easy to have stitches that are accurate on the top, but that miss the binding edge on the underside. The second line of stitches takes care of these cases and reinforces the final product.
While I was at it, I stitched across the seams where the black border met the large triangles, and along the color borders between the inner triangles. This sort of stitching is what gives it that classic quilted look, and also keeps each triangle together flat as it flexes. Try to use one long line for all your quilting stitches; you want as few loose thread ends as possible.
Step 5: Cut head opening, assemble tetrahedron
Using a color of thread that matches your binding, sew the edges together. Place triangles back to back (right sides out) and simply stitch along the edge. Though this will create a lip on the outside (showing edge) of the final product, because the triangles are already finished with binding I consider it aesthetically acceptable. Repeat process with the final triangle and the last two edges. After the edges are sewn together you should have a soft pyramid, almost capable of standing on its own.
Step 6: Initial fitting
Step 7: Create wire frame
Make three wire triangles the size of the tetrahedron sides and duct tape them together into a pyramid. Make absolutely certain that all sharp edges are firmly duct taped in place so that there are no unpleasantly pokey parts to injure your cat. Forming the pyramid out of three finished triangles has the benefit of creating nice smooth pieces, and also having two wires along each edge will give it extra support because coat hanger wire isn't that strong.
When the frame is ready simply pull the cloth over it and use safety pins or basting stitches to hold it in place. You don't want to permanently attach the frame because you may want to wash the costume in the future. All that you need is something to hold the bottom edge of the cover to the bottom edge of the frame, and safety pins hidden on the inside work perfectly for that.
Step 8: Final fitting
At first I was worried that my cat would be unhappy wearing the costume, but as it turns out he really likes it. Like many cats, he's got a strong instinct to sit inside of things so even when I took the costume off of him he got right back in. I would worry about him injuring himself if he wore it while I wasn't directly supervising him, but he definitely seems to appreciate the concept. Also, he appears to be able to walk around freely while wearing the costume, which is adorable!
While your cat is not wearing the tetrahedron it can be placed on its side to make a quilted cat tent-nook-bed thing, which both my cats (even the one that's far too skittish to be costumed) like very much.