Yes, my cage is built from cheap grids and coroplast and has 6 inch sides. Some people even make the sides higher than that. I also use a fleece bedding system, since shavings are so expensive and messy and it would take a truckload of it to fill my cage and a dumpster to carry it out.
Guinea Pig Cages, Your Cavy At Home if you go to the "gallery" you can see hundreds of cage pictures that people have built using inexpensive grids and coroplast.
CavyMadness great place for new pig owner
Index of / must read for all pig owners
Guinea Lynx :: A Medical and Care Guide for Your Guinea Pig go to the "care guide" for an extensive lesson in guinea pig care.
You will find that 90 percent of guinea pig owners on all guinea pig forums have now built CC cages rather than put pigs into tiny little litterbox sized pet store cages. So it's worth looking into.