With the spread of emerging services, multi-dimensional extreme performance requirements have been put forward for the sixth generation (6G) networks. The integration of sensing, communications, and computing (ISCAC) is expected to transform the 6G networks from simple transmission pipelines to smart infrastructures with enhanced capabilities. To help the 6G networks live up to their potential, we firstly design a three-dimensional ISCAC network architecture from the perspectives of network space, horizontal functionality, and vertical functionality. Next, we propose two performance indicators for the ISCAC network to map the multi-dimensional resources into the same evaluation system. Based on the proposed indicator, an AoI-enabled resource management mechanism is developed. Finally, performance evaluations are carried out and the time average expectation of AoI can be reduced by up to 36.39% compared with the existing mechanism.