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.

The definitive website for many models is Meenakshi Mukerji's Intersecting Planes Gallery — check it out! Instructions for many models are available for free. This article by Meenakshi Mukerji is helpful for assembling some of the models by her.

Blintz Icosidodecahedron by Tung Ken Lam: PDF Instructions (6 Pentagons)

VWXYZ: Photographic Instructions.

Book: Ornamental Origami by Meenakshi Mukerji (2008, 154 pages) has instructions for all her Intersecting Planes models.