What does triple-hollow construction mean? I've got a set of Sun Rhynolyte rims and in the features it says they have a  triple-hollow construction. What does that mean?
When a rim is extruded, the shape of the material can give added strength to the rim.
There are many rim types, but the two most common are single-walled and double walled. A single walled rim uses a simple U shaped extrusion. A double-walled rim adds a cross brace across that U shape, creating a D-shaped extrusion.
Triple hollow construction add extra cross-bracing to that D shape, resulting in more than one hollow area in the extrusion. It is supposed to add strength to the rim. Compare for example the following image from Sheldon Brown:

Thus the name.