Many quarter system schools do not have the December mini-term, but just start the autumn term later (e.g. late September). At those schools, the summer term allows for a normal length (10 week) quarter (hence the name quarter system).
Here are some other quarter system academic calendars:
http://www.registrar.ucla.edu/calendar/acadcal15.htm
http://www.washington.edu/students/reg/1516cal.html
https://studentaffairs.stanford.edu/registrar/academic-calendar-1516
https://www.deanza.edu/calendar/
Quarter versus semester system may affect student athletes, since it may affect how much of the academic year overlaps with the sports season. For example, a football player would find that football season overlaps with only 1/3 of the normal academic year at a quarter system school, versus 1/2 of the normal academic year at a semester system school. So a football player serious about academics may find the quarter system to be more advantageous.