  Tangible interfaces in mixed reality (MR) environments allow for intuitive
data interactions. Tangible cubes, with their rich interaction affordances,
high maneuverability, and stable structure, are particularly well-suited for
exploring multi-dimensional data types. However, the design potential of these
cubes is underexplored. This study introduces a design space for tangible cubes
in MR, focusing on interaction space, visualization space, sizes, and
multiplicity. Using spatio-temporal data, we explored the interaction
affordances of these cubes in a workshop (N=24). We identified unique
interactions like rotating, tapping, and stacking, which are linked to
augmented reality (AR) visualization commands. Integrating user-identified
interactions, we created a design space for tangible-cube interactions and
visualization. A prototype visualizing global health spending with small cubes
was developed and evaluated, supporting both individual and combined cube
manipulation. This research enhances our grasp of tangible interaction in MR,
offering insights for future design and application in diverse data contexts.
