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Many current intrinsically interpretable machine learning models can only handle the data that are linear, low-dimensional, and relatively independent attributes and often with discrete attribute values, while the models that are capable of handling high-dimensional nonlinear data, like deep learning, have very poor interpretability. Based on the geometric characteristics, a new idea of accurately wrapping the data region with minimum-volume geometry is proposed for pattern classification. The Variance Hyper Rectangle (VHR) model presented in this paper is a realization of the idea. The VHR model uses the minimum-volume hyper rectangles, obtained through projection variance calculation, to wrap the regions occupied by a category of data, hence it has strong and clear geometric interpretability. In addition, the VHR model is well suited for large data volume, as it approaches the linear complexity in both time and space. Extensive qualitative and quantitative experiments are performed on seven real-world data sets, demonstrating that VHR outperforms the state-of-the-art interpretable methods while running quickly. [Display omitted] • VHR has strong geometric interpretability, and is much reliable and trustworthy. • VHR can provide a clear range of values in each direction for a category of data. • VHR naturally supports incremental learning without any extra processing. • VHR has great performance and stability, and is able to handle big data. [ABSTRACT FROM AUTHOR]