Rings circle the corners. Each of the 52 corners wears 32 rings: ring 1 is the few tiles touching the corner, ring 32 runs along the far edges of the faces that meet there. A turn slides a ring one face round its corner.
Turn a ring by swiping along it on the dial, with the ↺ ↻ buttons, or by dragging a tile on the 3D puzzle. Every tile rides three rings, one round each corner of its face, and the direction you drag picks which.
Pick a corner with ‹ ›, a corner badge on the dial's rim, or a tap on the puzzle near that corner. Cap turns every ring from the corner out to the one you touch.
Look around by dragging the space around the puzzle (or right-drag, or two fingers). Scroll or pinch to zoom in on the tiles; double-tap to reset.
Keys:[] corner, ↑↓ ring, ←→ turn, C cap, Ctrl+Z undo.
The solid is the convex hull of 52 points spread as evenly as a sphere allows: the lowest-energy arrangement of 52 like charges from the Thomson problem. That gives 100 near-equal triangles, with 5 meeting at 12 corners and 6 at the other 40.