Cut four 1/2-inch-thick diagonal slices from the cucumber and then quarter each slice. Set the cucumber pieces on a large serving platter and season with 1/4 teaspoons each salt and pepper.
Top each with a piece of feta and then an olive half. Stab a toothpick through a tomato half and then thread through one of the cucumber stacks, pushing the toothpick down to secure it. Drizzle with the olive oil, sprinkle with some more black pepper, and serve.