This is a simple python solver for The Genius Star, a tiling puzzle made by the Happy Puzzle Company. The game involves tiling a star-shaped grid of triangles with a set of polyiamond pieces. Seven dice are rolled to indicate certain triangles which are blocked, and the other pieces must be fitted around these blocks. The tiling problem can be cast as an exact cover problem and the code here uses the python xcover package to do the solving. A good introduction to the theory behind the exact cover formulation can be found in Donald Knuth's paper.
The code requires python 3.7 or higher with the numpy, matplotlib, and xcover packages. The GUI requires the nicegui package.
from genius_star import Game
roll = [4, 10, 15, 18, 28, 33, 37]
game = Game(roll)
solution = game.solve()
solution.plot()
There is a Jupyter notebook describing the game and algorithm, which can be run directly in a web browser using services such as Colab or Binder. 
There is a web-based GUI for the solver, which can be run with
python3 gui.py
or by visiting https://geniusstar.johnrudge.com.
solve_all.py performs an exhaustive search of all 165,888 possible puzzles from rolling the dice. It takes around a minute to run, and shows that 97,422 of the combinations can be solved with a star (58.7%, slightly higher than the manufacturer's quoted figure of 57.4%). The routine exploits the symmetry of the board, namely that some dice rolls lead to puzzles which are reflections or rotations of other dice rolls e.g. the roll [4, 10, 15, 18, 28, 33, 37] is equivalent to [1, 7, 13, 22, 29, 31, 38]. Accounting for symmetry there are 24,192 unique puzzles that can be obtained with the dice (of which 14,149 have the star).
If you can place the blockers anywhere on the board there are many more possible puzzles, but they do not all have solutions. There are 73,629,072 possible placements of the seven blockers, of which 51,837,678 are solvable puzzles (70.4%) and 22,651,032 have the star (43.7% of the solvable). Accounting for symmetry, there are 6,140,978 blocker placements, with 4,322,975 solvable and 1,888,833 with the star. The puzzles given by the dice represent only 0.32% of all the solvable puzzles by placing the seven blockers on the board.
This software is licenced under the GNU Lesser General Public License v3.0.
John F. Rudge