recently I realized that you can turn a cube into a tetrahedron by slicing off four corners. each corner becomes an equilateral face, but the cool part is that each edge corresponds to the diagonal of a cube face. six edges. guess what that means? edge-to-edge, tetrahedra "tesselate" like cubes! quotes because they would leave big octahedron-shaped gaps around all those corners you sliced off earlier. but you wouldn't see the gaps, so maybe you could call it "visual tesselation". is that a thing?
interestingly, a visual tesselation of tetrahedra requires two orientations of tetrahedra like a checkerboard (every edge-to-edge contact involves a reflection). a voxel system would have polygons facing in eight directions. two more than six. so if you want to try to make your game look somewhat less blocky and more organic, tetrahedron-voxels could give that feature a boost. not to mention that with reduced polygons you could afford higher resolution.
PS: all the above I have learned purely through mental visualization. if you try actually playing with matrices of tetrahedra as I described, PLEASE toot me back! I want to see it. maybe I'll write something up, but my coding time is limited these days.
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