Hyperlinking: A TriCycle is a cycle of 3 linked hypertext pages. It is the smallest cycle possible.

A TriCycle can represent movement through 3 dimensions.

The form of 3 is essential in all: the Trinity, Brahma, Vishnu, Shiva, Time, Space, Matter, Creation, Existence, Destruction, Langue, Parole, Language, etc.

''What? How is the "form of 3" specifically related to time?''

Is is also a motorcycle with 3 wheels...

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Stating the obvious:

You can have cycles of length 1 (see TriCycle) or 2. Link cycles of length 3 don't necessarily have anything to do with the 3 (macroscopic, spacelike) dimensions of our universe.

Some high-profile sets of 3 may be the way they are because people like to arrange things in threes rather than because the nature of things is to prefer triplets. 

Time
* "Time, Space, Matter": these three things are not on an equal footing. "Time and Space", yes, to some extent; but matter is just something that occupies time and space, and separating space and time is a bit arbitrary anyway. So it could have been, say, "Space-time, matter" (2 things) or "Space, time" (2 things) or "Time, space, matter, energy" (4 things), or "Space-time, matter, information" (3 things, but a different 3) or any number of other possibilities. Why choose "time, space, matter"? Because it's a triplet, and triplets sound good.
* Yesterday (Past), Today (Present), and Tomorrow (Future) This is a triplet of how we perceive and act out our existance. We have a view of what was, the action space of now, and a perception of what might be. All three of these things are somewhat changeable in nature. We can change our view of past events, we can change our behaviour in present circumstances, and we can alter our plans of shaping our future.  

Likewise for "Creation, existence, destruction". How about "creation, stability, change, destruction"? Or "creation, destruction"? Or, again, lots of other possibilities?

Oh, and a tricycle needn't have an engine; indeed, most of the tricycles I've seen have been purely human-powered.

-- GarethMcCaughan

''He might be referring to GraphTheory, in which a C3 is indeed the smallest cycle. A C2 is not distinct from an (undirected) edge. And a C1 isn't distinct from a node.''