This plant is known as euphorbia tirucalli, or more commonly as the pencil or stick cactus. Don’t be fooled–it’s not a cactus but a succulent. As such, it needs a little more water than a cactus would–every couple of weeks in the winter (when our homes are drier, succulents need more water. In the humid summers, they need less). The Euphorbia family is huge and includes a number of common succulents, as well as many that folks think of as perennials, and of course, the poinsettia. The common element is milky sap in hollow stems. Some may find this irritating if it comes into contact with skin.
What makes this plant great is its sculptural form. What makes it lovely for winter is the fresh green chartreuse new growth on its tips. Enjoy!