Connecting the 2D appearance of minerals in thin section to their 3D crystal forms is a common challenge for undergraduate mineralogy students. Complex crystals (e.g., dihexagonal prisms) may appear simple in thin section, while simple forms (e.g. tetragonal prism) can produce unexpected polygonal sections. Understanding these relationships requires penetrative thinking, a spatial reasoning skill rarely practiced explicitly in geoscience curricula.
Mathematically, a planar section of a convex polyhedron can yield a polygon with up to F + 1 sides (F = number of faces), but the distribution of polygon types for all crystal forms has not been systematically quantified yet. This limits the accuracy of 3D crystal size distributions (CSDs) derived from 2D sections, which relies upon correction factors derived from geometrical simplifications.
To address these challenges, we developed XtalSlice, a MATLAB-based tool with a GUI that generates all 48 mineral crystal forms and stochastically samples n random planar cuts. It visualizes resulting polygonal sections and calculates their relative frequencies, supporting both quantitative analysis and classroom exercises in penetrative thinking.
We developed a lab utilizing XtalSlice in an introductory mineralogy course. Student feedback was positive, especially after the introduction of the GUI in the second run. Unexpectedly, students initially interpreted the variability of repeated runs as a coding error, which became a teachable moment on randomness, sampling variability, and the law of large numbers.
Future work will validate the algorithm through systematic synthetic slices collected taken through nanoCT 3D scans of natural samples, which could additionally be incorporated into the laboratory experience for undergraduate students.