For want of a better name, I call these "meet in the middle" pop up cards.
Half of the design is cut from either side of the card and the two pieces are slotted together.
This card is really an elaborate variation of the slotted X mechanism.
The slotted X is covered in How to Make Pop Up Cards, Lessons 11 - 15 .
How to make the pile of hearts Valentine pop up card
Download and cut out template.
Download file set: PDF, DXF, SVG (how to use my SVG files in Cricut Design Space), Silhouette Studio.
Files download for free; pay what you wish for the tutorial and to support this site. Suggested contribution for this project is $1.99.
Remove the large heart that lies on the center fold. Use it on the front of your card or discard.
Crease the fold lines at the heart bottoms, folding both piles of hearts toward the center foldline.
The card will close better if you cut the two halves of the (white) card apart at the center fold and glue them to the base card separately. I did not do this, and I got a wrinkle. (UPDATE 2/7/2014: Cutting files have been corrected to cut rather than score on center fold.) Here's one by Molly Lee to show you what I'm talking about.
Optional: back the cut out with patterned paper before gluing to the base card. I used a red striped paper. Be careful not to get glue on the hearts, just the part they were cut from!
Glue cut-out part (white) to base card (red). Again, take care not to get glue on the hearts.
Pull the hearts toward each other and slot together above the center fold of the card.
The card lies completely flat when opened.
More about how this card works for the mathematically inclined....
The measurement from the center fold of the card to the crease line of the hearts is the same on both sides of the center fold. (Shown in red.)
If you draw a line from the end point of one slot to the end point of the other, you have a straight line perpendicular to the center fold. And each end point is at equal distance from the center fold. (Shown in blue).
Extreme Cards and Papercrafting: pop up cards, movable and mechanical cards, digital crafts and unusual papercrafts.