The　three-dimensional　(3D)　chromosomal　structure　plays　an　essential　role　in　all　DNA-templated　processes,　including　gene　transcription,　DNA　replication　and　other　cellular　processes.　Although　developing　chromosome　conformation　capture　(3C)　methods,　such　as　Hi-C,　which　can　generate　chromosomal　contact　data　characterized　genome-wide　chromosomal　structural　properties,　understanding　3D　genomic　nature-based　on　Hi-C　data　remains　lacking.　Here,　we　propose　a　persistent　spectral　simplicial　complex　(PerSpectSC)　model　to　describe　Hi-C　data　for　the　first　time.　Specifically,　a　filtration　process　is　introduced　to　generate　a　series　of　nested　simplicial　complexes　at　different　scales.　For　each　of　these　simplicial　complexes,　its　spectral　information　can　be　calculated　from　the　corresponding　Hodge　Laplacian　matrix.　PerSpectSC　model　describes　the　persistence　and　variation　of　the　spectral　information　of　the　nested　simplicial　complexes　during　the　filtration　process.　Different　from　all　previous　models,　our　PerSpectSC-based　features　provide　a　quantitative　global-scale　characterization　of　chromosome　structures　and　topology.　Our　descriptors　can　successfully　classify　cell　types　and　also　cellular　differentiation　stages　for　all　the　24　types　of　chromosomes　simultaneously.　In　particular,　persistent　minimum　best　characterizes　cell　types　and　Dim　(1)　persistent　multiplicity　best　characterizes　cellular　differentiation.　These　results　demonstrate　the　great　potential　of　our　PerSpectSC-based　models　in　polymeric　data　analysis.