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You run into Crush's father, Mr. Turtle, who is just now repainting his shell. He thinks your submarine improvements are totally wicked and wants them immortalized on his shell (at least until he repaints again), but he needs it to match the style of his new décor. He has some rules that he gives you for how to tattoo the improvements onto his shell. He gives you pieces of a map for the shell as he completes his paint job (turtles are a bit scatter-brained so he can't give you the whole map at once). The rules are coded on each hex of his shell. On top of tattooing letters onto his shell's hexes, Mr. Turtle wants you to darken some of the edges of the hexes as part of the ancient turtle art of shellomancy, where you can tell your future from the patterns on the shell.
|Each of your sub improvements must be spelled out in a continuous, non-crossing path in uppercase letters on his shell with one letter in each hex.|
|This letter is a vowel (Y counts as a vowel). If it is A, then it has 6 edges darkened, otherwise it has 2.|
|This letter is a Roman numeral. If it is I, it has 4 edges darkened. L and D have 3 edges, V and X have 2 edges, and C and M have 1 edge.|
|The letter has 2-fold rotational symmetry. If it is an N, it has 4 edges darkened.|
|This letter contains a horizontal mirror plane. If no other edge rules apply, the letter has 0 edges darkened.|
|This letter contains a vertical mirror plane. If it is H or W, it has 3 edges. If no other edge rules apply, the letter has 0 edges darkened.|
|This letter encloses some space (e.g. O). If this letter is P and no other edge rules apply, then it has 1 edge darkened.|
|This letter is a multiple of 3 (A = 1). If it is C (i.e. the first such letter), it has 2 edges darkened.|
|This letter has no symmetry. If no other edge rules apply, the letter has 0 edges darkened.|
|The letter has as many edges darkened as its value in Scrabble (turtles love Scrabble).|
|Of the adjacent letters, n are also immediately adjacent to this letter in the alphabet, where n is the number in the circle.|
|This letter has as many edges darkened as the number of adjacent vowels (Y counts as a vowel).|
|There must be exactly 52 darkened edges in total on the shell and all contiguous collections of edges must contain at least three edges.|
For reference, the letters with rotational symmetry are H, I, N, O, S, X, and Z. The letters that contain a vertical mirror plane are A, H, I, M, O, T, U, V, W, X, and Y. The letters that contain a horizontal mirror plane are C, D, E, H, I, O, and X. The letters with no symmetry are B, F, G, J, K, L, P, Q, and R.