The Tertiary Phase, Quandary Phase, Quintessential Phase and Hexagonal Phase are respectively the third, fourth, fifth and sixth series of The Hitchhiker's Guide to the Galaxy radio series. Produced in 2003, 2004 and 2018 by Above the Title Productions for BBC Radio 4, they are radio adaptations of the third, fourth, fifth and sixth books in Douglas Adams' The Hitchhiker's Guide to the Galaxy series: Life, the Universe and Everything; So Long, and Thanks For All the Fish; Mostly Harmless and And Another Thing....
These radio series consisted of a total of twenty episodes, following on from the twelve episodes from the original two series (the Primary and Secondary Phases) which originally aired in 1978 and 1980.
The producers chose not to continue the ordinal sequence established by the Primary, Secondary and Tertiary phases. If they had done so, the fourth, fifth and sixth series would have been termed quaternary, quinary and senary. Humorously, they chose "Quandary", which means "dilemma", "Quintessential", which today means "the most perfect example of something" (although the original meaning of quintessential was "fifth element"), and "Hexagonal", which refers to hexagonal phases.