In the NSX-T Data Center Architecture, the three different types of planes are the Management Plane, the Control Plane, and the Data Plane. The Management Plane is responsible for providing the management UI and APIs to configure, monitor, and operate the NSX-T infrastructure. The Control Plane is responsible for computing the runtime state based on configurations and propagating this state to the Data Plane. The Data Plane is responsible for handling the actual packet forwarding based on the runtime state received from the Control Plane. There is no defined 'Network Plane' or 'Routing Plane' in the VMware NSX-T Data Center Architecture.