We introduce the Persistent HyperOcTree (PHOT) to handle the 4D isocontouring problem for large scale time-varying data sets. This novel data structure is provably space efficient and optimal in retrieving active cells. More importantly, the set of active cells for any possible isovalue are already organized in a Compact Hyperoctree, which enables very efficient slicing of the isocontour along spatial and temporal dimensions. Experimental results based on the very large Richtmyer-Meshkov instability data set demonstrate the effectiveness of our approach. This technique can also be used for other isosurfacing schemes such as view-dependent isosurfacing and ray-tracing, which will benefit from the inherent hierarchical structure associated with the active cells.