I could keep it for the fortnightly links, but the Hodge diamond lepidopterist in me is too excited. The Hodge numbers for O'Grady's sporadic 10-dimensional example have been computed, by Mark Andrea de Cataldo, Antonio Rapagnetta and Giulia Saccà in their paper The Hodge numbers of O'Grady 10 via Ngô strings.

I have nothing useful to say about the proof, as it is far outside my comfort zone. But I did add it to my collection of butterflies Hodge diamonds. In its full glory it looks like: \begin{array}{ccccccccccccccccccccc} & & & & & & & & & & 1 & & & & & & & & & & \\ & & & & & & & & & 0 & & 0 & & & & & & & & & \\ & & & & & & & & 1 & & 22 & & 1 & & & & & & & & \\ & & & & & & & 0 & & 0 & & 0 & & 0 & & & & & & & \\ & & & & & & 1 & & 22 & & 254 & & 22 & & 1 & & & & & & \\ & & & & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & & & & \\ & & & & 1 & & 23 & & 276 & & 2299 & & 276 & & 23 & & 1 & & & & \\ & & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & & \\ & & 1 & & 22 & & 276 & & 2531 & & 16490 & & 2531 & & 276 & & 22 & & 1 & & \\ & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & \\ 1 & & 22 & & 254 & & 2299 & & 16490 & & 88024 & & 16490 & & 2299 & & 254 & & 22 & & 1 & \\ & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & \\ & & 1 & & 22 & & 276 & & 2531 & & 16490 & & 2531 & & 276 & & 22 & & 1 & & \\ & & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & & \\ & & & & 1 & & 23 & & 276 & & 2299 & & 276 & & 23 & & 1 & & & & \\ & & & & & 0 & & 0 & & 0 & & 0 & & 0 & & 0 & & & & & \\ & & & & & & 1 & & 22 & & 254 & & 22 & & 1 & & & & & & \\ & & & & & & & 0 & & 0 & & 0 & & 0 & & & & & & & \\ & & & & & & & & 1 & & 22 & & 1 & & & & & & & & \\ & & & & & & & & & 0 & & 0 & & & & & & & & & \\ & & & & & & & & & & 1 & & & & & & & & & & \\ \end{array}