Use this PVC fitting for gravity-fed waste elimination system. The Charlotte Pipe 12 in. DWV PVC Hub x Hub Coupling in Home Depot site describes the product details with all necessary specifications. It is convenient to install.
Use pre cut six inch PVC pipe for this project. You should use a PVC cement glue to join them together. It is also a good idea to sand down the edges before you start gluing. You can paint them before you attach them.