The sphere carries a circle packing: one circle per vertex of a triangulation, with two circles tangent exactly when their vertices share an edge. The dark geodesic arcs are the edges. Each circle is colored by its degree, the number of circles it touches. A circle that is not degree 6 but too small to see gets a ring in its color.
Flip an edge by clicking it (on a touch screen, tap once to select and again to flip). The two triangles beside the edge form a quadrilateral, and flipping swaps its diagonal: the two circles on the edge let go of each other while the two opposite circles are drawn together until they touch. The packing flows continuously from one packing to the next.
Reach the goal's degree pattern. Any packing with the right number of circles of each degree wins; it need not be the one in the preview. For the buckyball, that means every circle touches 5 or 6 others, with exactly twelve 5s.
Excess is the total degree above 6. It is 0 only when no circle has more than 6 neighbors. Scramble is the number of flips used to make the puzzle, so a solution at least that short exists.
Drag the sphere to roll it (the point you grab stays under the cursor) · drag outside it to spin · scroll or pinch to zoom · U undo · H hint · V reset view
Based on Ken Stephenson's flip puzzle in CirclePack. The motion is flip-and-flow (R. Connelly and S. Gortler, Packing disks by flipping and flowing, 2021; J. C. Bowers, A proof of the Koebe–Andre'ev–Thurston theorem via flow from tangency packings, 2020): every edge except the flipped one stays tangent while the new pair is pulled together. Every packing in the game, including the scrambled starts, is built this way from the regular solids.
This puzzle draws the sphere with WebGL2, which this browser does not provide.