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The triakulus is equal to $$3\&3\&3$$ or $$\{ 3,3 /2 \}$$ or $$\{L,1\}_{3,3}$$ using the array of operator and BEAF.[1] Since the array of operator solves from left to right, $$3\&3\&3 = \{ 3,3,3 \} \& 3$$ = $$3 \uparrow\uparrow\uparrow 3 \& 3$$, a pentational array. The structure of an array which defines triakulus is supposedly X^^X^^X. Triakulus is intended to have tritri entries.

It must be remembered that although it has tritri entries, a triakulus is in no way the same thing as a linear array with tritri repetitions of 3. That would be dupertri, which is a much smaller number. One of the major challenges behind defining this level of BEAF would be successfully conceive a representation of triakulus that captures all its tritri entries while setting it apart from a dupertri.

If defined, this would be the smallest number named by Jonathan Bowers which lies in the pentational-array range.[2] This is the first Bowerism which is not well-defined.

## Approximations

Since it is not defined by now, the following approximation is just an expected value under climbing method (strong bound):

Notation Approximation
Bird's array notation {3,3 [1 [1 [2] 2 ¬ 2] 2] 2}
Fast-growing hierarchy $$f_{\varphi(\varepsilon_0,0)}(3)$$
Hardy hierarchy $$H_{\varphi(\varepsilon_0,0)}(3)$$

## Sources

Tritri series: tritri · tritet · tripent · trisept · tridecal · grand tridecal
Tetratri series: tetratri · supertet · general(plex)
Pentatri series: pentatri · superpent · pentadecal(plex)
Hexatri series: hexatri · superhex · hexadecal(plex)
Heptatri series: heptatri · supersept · heptadecal
Iteral series: superoct · octadecal · superenn · ennadecal · iteral · ultatri
Dupertri series: dupertri · duperdecal · truperdecal · quadruperdecal
Latri series: latri · emperal(plex) · hyperal(plex) · diteral(plex) · admiral
Dutritri series: dutritri · dutridecal
Dimentri series: dimentri · dulatri · trilatri · trimentri
Triakulus series: triakulus · tridecatrix
Big boowa series: big boowa · great big boowa · grand boowa
Tiaokhiao's extensions: trihex · trioct · triennet · triundecal · tridodecal · tritriplex · tritriplexian · grand tritri · tetrapent · tetrahex · grand tetratri · octatri · enneatri · decatri · undecatri · dodecatri
RedBandServerYT's extensions: tridecalplex

Jonathan Bowers' array of series