I thought making a slant-sided leprechaun hat for St. Patrick's Day would be a simple variation of a tabletop type pop up cake or coffee cup. But no, because you can't collapse an angled shape in the same way as a straight sided shape.
After much gnashing of teeth and shredding of paper, I realized the side struts and the center strut, which hold up the top of the hat and provide the pop-up power, must be the same length. The side struts, therefore, can not be adhered vertically to the inside of the hat--because the hat sides are longer than the distance straight up the center. They have to stand free.
Therefore, the hat shape is not as stable as a straight sided shape. The top of the hat doesn't always want to settle into place when the card pops open. I compensated for this by making the hat a little taller. The hat top sits down inside the hat rather than resting on the top edge.
How to make a pop up leprechaun hat
The large curved piece is the hat side. You will want to pre-curl this piece before assembly to encourage it to form as round a shape as possible when popped up. Pull the piece against a ruler, or the edge of a table, (the same way you would curl ribbon) to make a slight curve in the paper. (See step 4 of these instructions for an illustration.)
I also like to curve the outside edge of the hat top (the smaller circle) in the same way. Use the flat side of a pen and pull very lightly from the center of the circle to the edge, working around the circle, getting the outside edge to curl under just the smallest bit all the way around.
Fold hat side on crease lines, matching tabs. Glue overlap.
Pre-curl the hat band slightly and glue to hat. Do not glue buckle and shamrock yet. They get in the way and you'll want to decide the placement on the finished piece.
Spread adhesive on the strut piece as shown and then fold on the vertical score line.
Crease the score lines to create the top,center and side struts.
Measure and mark the center of the hat top (smaller circle). Pencil a line through the center point, parallel to the score line.
Adhere the strut tops to the hat top, centered on the pencil line. Be sure the adhesive completely covers the section of strut that you are gluing, particularly near the crease line indicated by the arrow. You can add a little piece of tape across the glued part of the strut if you like, it won't show.
Slide tabs of center strut through the slit in the hat bottom (large circle). Slide side struts through the side slits of the hat bottom.
Spread the tabs out and glue. The side strut tabs must be turned toward the center of the circle. They can go under or on top of the center strut tabs, it doesn't matter. Again, you can tape these for added security if you like.
Collapse this center piece and slip it up inside the hat side piece.
Slide the tabs of the hat side through the side slits (the same slits the side struts went through). Fold up the tabs toward the outside edge of the large circle. Adhere. Tape if you like.
Add buckle and shamrock to the hat brim.
Glue the hat into your base card, matching center folds.
Here's a variation by Rachel--a yogurt cup.
Extreme Cards and Papercrafting: pop up cards, movable and mechanical cards, digital crafts and unusual papercrafts.