An "Intersecting Planes Model" gives the impression of identical planar figures intersecting each other. Examples:
Tung Ken Lam designed "Four Intersecting Triangles" in 1999. His model aroused plenty of excitement in the origami community. A flurry of activity ensued. Within a few years, Meenakshi Mukerji, Francis Ow and others discovered twenty-odd new models. Meenakshi Mukerji's models are especially spectacular: Check out her gallery! Tung Ken Lam's WXYZ is charming — sturdy and esthetically pleasing. This should definitely be the first model that you assemble.
(Click to enlarge)
The simplest "intersecting planes model" is WXYZ by Tung Ken Lam.
Step 1: Familiarize yourself with Origami symbols like mountain / valley folds.
Step 2: Make 12 units of the WXYZ Model, as per instructions in the image (click to enlarge). Excellent Photographic Instructions are also available. Or you may watch the videos below.
Step 3: Assemble 12 WXYZ units together, as per instructions. You may also watch the videos below.
Step 4: Take a picture of your model and display it on the web!
Step 5: Make other Intersecting Plane Models or design one of your own.