with a PoE injector adapter (RJ-45 plug & 2.1×5.5 mm power jack to RJ-45 jack) going for about 80 cents, and a DC-DC buck converter that can handle the input of 12V for about 50 cents.

A PoE injector is also called a "PoE adapter." See PoE. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction requires permission.