1. Rinse the rice. In a saucepan with a tight fitting lid, add the rice and cold water. Let stand 15 minutes then bring to a boil, cover and reduce heat. Cook for about 10 minutes until the water is absorbed.
2. Redice the heat to low and simmer for another 5 minutes. Remove from heat and let the rice stand, for 5 minutes. Transfer the rice to a large platter.
3. Mix together the vinegar, sugar, salt and mirin, and pour over rice while mixing with a fork. Cool to room temperature.
4. In a small bowl, combine wasabi and water.
5. Lay one sheet of seaweed on work surface and with dampened hands, spread 1 cup of rice over the seaweed leaving a 1 inch strip along the top.
6. Using 1/4 of the wasabi mixture paint a stripe on the rice, 1 inch above the bottom edge. Arrange 1/4 of the crab over the stripe. Arrange 1/4 of the avocado slices next to the crab and then 1/4 of the cucumber next to the avocado.
7. Beginning at bottom edge, carefully roll the seaweed and it;s contents jelly roll style. Moisten the top edge to seal.
8. Continue in the same manner for the remaining three sheets of seaweed.
9. Using a sharp knife slice into 1 inch pieces.
10. Serve with wasabi and soy sauce for dipping.