For the cake:

1. One hour before starting the cake, grate the zest of both limes and reserve in a bowl wrapped in plastic.
2. Juice both limes and add to a bowl with the coconut. Mix to moist evenly and let soak for 1 hour.
3. Preheat oven to 325º.
4. Butter or spray a non-stick 9-inch cake or pie plate with high sides.
5. In a large bowl, sift flour and baking powder. Make a well in the center and add sugar, butter, eggs, coconut with juice and lime zest.
6. Beat with an electric mixer for 3 or 4 minutes, until creamy.
7. Pour into prepared pan and bake for 35 to 40 minutes, until a tester inserted in center comes out dry. 
8. Transfer to wire rack, let cool for 5 minutes and unmold. Let cool completely before icing.

For the icing:

1. On a shallow plate of bowl, peel the lime, exposing the green part, and cut in segments, as shown here. Be sure to gather the pulp and the juice.
2. Mix the powdered sugar in a bowl with the lime juice only first. When that is mixed add half of the segments. Some will crush and some will remain whole.
3. When the cake is cool, drizzle the icing on top, letting it drip to the sides. Arrange the rest of the segments on top.