The mathematics of Septoku

Septoku is a Sudoku variant invented by Bruce Oberg, played on a hexagonal grid of 37 cells. We show that up to rotations, reflections, and symbol permutations, there are only six valid Septoku boards. We show that the minimum number of starting seeds for a Septoku puzzle to have a unique solution is six. We generalize the puzzle to other board shapes, and devise a 6-seed puzzle on a star-shaped board with 73 cells that has a unique solution.