Various approaches to performing ray-triangle intersection tests for single triangles or clusters of triangles are presented. In some example implementations, the triangles are organized in tetrahedral clusters, and the ray-triangle intersection tests use plane data for sets of planes of the tetrahedral clusters. A triangle can be represented as three bounding planes. Further, in some example implementations, the same three bounding planes of a tetrahedral cluster can be used to represent one, two, or three triangles that define faces of that tetrahedral cluster. With this configuration, overall memory costs are reduced when the same plane data is used to represent multiple triangles, and operations to check for ray-triangle intersections are still computationally efficient.