Apert (from aperture) is the ten-day period during which the gates of a math are opened by the Great Clock, allowing people from outside the math to enter and for the avout to travel extramuros.
Maths are named for the intervals at which their Aperts occur:
Unarian: yearly; Decenarian: every ten years; Centenarian: every hundred years; Millenarian: every thousand years.
The same mechanism opens the day gate daily, but this is not considered Apert as ingress is strictly controlled and egress is only for heirarchs and those who are Thrown back or Evoked or those who are forsaking their vows and leaving of their own free will.
Once every thousand years, all of the gates open at once and there is a full Convox of avout during Apert, one goal of which is to review and revise the Dictionary as necessary. This Millennial Apert is the only time avout of all different maths may interact. The only other way between Aperts is for an avout to leave his or her math by way of a labyrinth or to be evoked along with avout of other maths, as happens to Fraas Erasmas and Jad during the events of Anathem.