  Hex-dominant mesh generation has received significant attention in recent
research due to its superior robustness compared to pure hex-mesh generation
techniques. In this work, we introduce the first structure for analyzing
hex-dominant meshes. This structure builds on the base complex of pure
hex-meshes but incorporates the non-hex elements for a more comprehensive and
complete representation. We provide its definition and describe its
construction steps. Based on this structure, we present an extraction and
categorization of sheets using advanced graph matching techniques to handle the
non-hex elements. This enables us to develop an enhanced visual analysis of the
structure for any hex-dominant meshes.We apply this structure-based visual
analysis to compare hex-dominant meshes generated by different methods to study
their advantages and disadvantages. This complements the standard quality
metric based on the non-hex element percentage for hex-dominant meshes.
Moreover, we propose a strategy to extract a cleaned (optimized) valence-based
singularity graph wireframe to analyze the structure for both mesh and sheets.
Our results demonstrate that the proposed hybrid base complex provides a coarse
representation for mesh element, and the proposed valence singularity graph
wireframe provides a better internal visualization of hex-dominant meshes.
