What can be said about a substance with a triple point above 1 atm?
Such a substance sublimes at one atmosphere pressure.
In a standard phase diagram for a single substance, the triple point is a single combination where solid, liquid, and vapor come together in a three-phase equilibrium. The liquid phase is found only above the pressure of the triple point. Below that pressure the solid and gas are in equilibrium without the liquid, so the solid sublimes instead of melting. Carbon dioxide, whose phase diagram is shown below, is one example. Image from http:/davidjohnnewhart.com/Chemistry.