The rapid development of wireless network shows a trend of increasing complexity of structure and multi-dimensional network resources. At the same time, the energy efficiency of future networks attracts more and more attentions and calls for green designs. These concerns motivate us to investigate energy-efficient networking in generic wireless network for solutions over multi-dimensional resource space. In this paper, we develop a joint optimization of scheduling and power control with multi-dimensional modeling. With this framework, transmission scheduling, routing, power control, radio and channel assignment will be jointly optimized to minimize energy consumption while guaranteeing flow demands of multiple commodities. In order to tackle the complexity issues raised from coupled resource dimensions and obtain a joint solution, we propose a novel decomposed approach. In particular, we leverage a multi-dimensional tuple-link based model and a concept of transmission pattern to transform the complex optimization problem into a linear programming (LP) problem. The LP problem however presents a very large problem scale, which is then countered by exploiting delay column generation technique. Furthermore, we propose a greedy algorithm to solve the sub-problem efficiently and derive the performance bound through solving its relaxed problem. Through numerical results, we demonstrate the benefit of joint optimization and analyze the effect of multi-dimensional resources on network energy efficiency.