Does every pure chemical substance admit a triple point?

Well, a quick internet search shows that not necessarily. For that to happen, a combination of pressure and temperature is needed where the vapor, liquid, and solid have the same Gibbs free energy.. Although it seems that most substances admit a critical point, this does not seem to be the general case. Most are substances such as water where there is a combination in which the three phases can coexist:

helium _has the following phase diagram, where there is no point where the three classic phases coexist: