Kaplan's work primarily focuses on applications of geometry and computer science to visual art and design.

[8] Kaplan's research work focuses on the application of computer graphics and mathematics in art and design.

In 2019, Kaplan helped to apply the concepts of Archimedean solids to protein assembly, and together with an experimental team at RIKEN demonstrated that these exotic geometries lead to ultra-stable macromolecular cages.

The discovery is under professional review and, upon confirmation, will be credited as solving a longstanding mathematical problem.

In May 2023 the team of Smith, Kaplan, Myers, and Goodman-Strauss posted a new preprint proving that the new shape, which Smith called a "spectre", is a strictly chiral aperiodic monotile: even if reflections are allowed, every tiling is non-periodic and uses only one chirality of the spectre.