Geometers is one name for those thought to be controlling the icosahedron. In English, the word "geometer" denotes a mathematician whose field of research is geometry. This name gained popularity because the ship has a diagram offering a proof of the Adrakhonic Theorem visible on its side. The Avout took this to mean the occupants had an interest in Geometry. In fact, the Geometers come from four different planets, and have two strong political factions.
Later, the term "Cousins" becomes more popular, once it is discovered that at least Lise is very similar in form to the people of Arbre.