In my opinion, a triangle model is still a triangle. Therefore, I believe that a triangle can be touched!

Quote from dictionary one: "A model is a man-made imitation of the objects being studied: layouts, images, diagrams, verbal descriptions, mathematical formulas, maps, etc. Models are always simpler than real objects, but they allow you to highlight the main points without being distracted by details."

Quote from dictionary two: "A mathematical model is a model of an object, process, or phenomenon, represented by mathematical patterns that describe the main characteristics of the modeled object, process, or phenomenon."

Thus, a model of an object simply cannot be the object itself. You can "touch" a model as much as you like, but a triangle consisting of points (and the segments that make it up are also formed by points) – unfortunately, you cannot. Because a mathematical point, although it is a component of objects, has infinitely small dimensions in space, i.e., its existence tends to zero.