Huh? I only see one diamond shape. There are two triangle shapes; one from the steering column to the seat post, and one from the seat post to the rear-wheel axle. They make up one diamond, not two.
What am I missing?
It took me a bit of searching but it does appear "diamond frame" bikes are a concept which then makes sense. Apparently some mountain biking applications or uses with more stress require a "double diamond frame".
That's what I could figure out though.
I also don't think they need to be exactly triangles, just as long as the nodes are generally connected via the same edges. Also sometimes the top and bottom bar don't meet at a single point on the steering post so that shape ends with with 4 sides.
edit:
Also, don't all of the designs have two arms in the back? Even the original "diamond frame" has the same rear tire attachment.