This paper discusses “stick hyperboloids” and three geometric questions related to their construction. These are physical structures made by assembling rigid physical rods that cross each other, creating an attractive model of a hyperboloid of one sheet. First, some educational, architectural, and artistic examples are illustrated. Then original results are explained concerning the spacing between the crossings, the angles for pre-drilling connector holes, and what exactly happens when the structure is flexed. These results almost certainly were discovered previously, but I could find no hint of them in the literature. In addition, I show a new form of paper hyperboloid model that emerged from this analysis.