Wash radishes, dry and slice using a mandoline or sharp knife about 1/4-inch thick, or cut into matchsticks or wedges. In a medium saucepan over medium heat, combine the vinegar, sugar, honey and salt and heat until ingredients are dissolved, about 2 minutes. Remove from heat. Stir in lime juice.* Place the radishes and garlic in a clean jar and pour the liquid into the jar. If you wanted more of a kick, you could add jalapenos as well. Leave about ¼ inch of room at the top. Cover, let cool, and refrigerate for at least 4 hours.
* This step can be skipped and simply place all of the ingredients together then put in jars and place in the refrigerator.