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Maybe a little too obvious but Darumakka and Hihidaruma are daruma dolls. The dolls are used sort of like good luck charms; they're made with blank eyes (or sometimes one inked in eye) and youre supposed to make a wish or set a goal to represent the first eye, and you fill in the second eye once your goal is met. It's less a "wish" charm and more like a reminder of incomplete aspirations. But the doll itself is based on the Bodhidharma, a buddhist mytho-historic monk. Among other things he was said to have reached a state of such deep meditation that he became like stone, and his limbs atrophied and fell off, which is part of why the shape of the daruma doll is what it is, and why the zen mode of Hihidaruma gains psychic type.
And the Japanese term for a snowman is Yuki-daruma. lit."snow daruma" hence the regional variant.