Many years ago, I saw instructions for making a decoration like this out of Christmas cards. I hadn't made one in years, but remembered the idea yesterday when I was taking down our cards from this year. My wife Erika really liked the result, and has asked me to do this each year so we can add these to our usual Christmas decor.
To make a Christmas card ball, you'll first need to make a pattern by drawing an equilateral triangle enclosed by a circle intersecting all 3 points. You'll probably want a ruler, compass, and protractor for this, to make sure your lines and angles are precise.
Cut out your circle, and trace it onto Christmas cards. You'll need 20 circles, each one enclosing some interesting bit of holiday art. Depending on the size of your circles and your cards, you may be able to get multiple pieces out of some cards.
(If you don't have enough cards, or don't want to destroy the ones you received from friends and family, then just buy a cheap package or two of blank cards from the store. The more variety, the better, and they'll be marked way down after Christmas.)
Cut out your circles, and trace the triangle onto the back side. Use a pen or the point of your scissors to score these three lines, then fold up the flaps toward the art side.
Fasten the flaps together using staples or glue, as shown in the photo. You will form an icosahedron (a 20-sided regular polygon) out of the triangles. It's probably easiest to build it in three parts--the two "tents" of 5 triangles at the top and bottom, and the ring of 10 triangles between them--then join those sections together.
To hang it up, thread some ribbon or yarn through the vertices of the ball, or punch a hole in one of the flaps.