2 medium pink grapefruits, cut into 12 wedges each, plus 1 peeled and broken into segments
8 ounces vodka
1 cup fresh lime juice
Rock salt, for grating
Combine the sugar and 2 cups water in a medium saucepan. Bring to a boil and shut off the heat. Transfer to a bowl to cool. Refrigerate.
Combine half of the cucumber slices with all of the unpeeled grapefruit wedges in a large bowl. Muddle them by pressing down on them with a whisk to extract the juices and lightly crush the cucumbers. Add the vodka, lime juice, simple syrup and 2 cups lightly crushed ice. Pour into a pitcher and grate salt over the top. Add the peeled grapefruit segments and remaining cucumber slices. Alternatively, serve from the pitcher and grate the salt as you pour the individual drinks.