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Trihex is equal to $$\lbrace6,6,6\rbrace$$ or $$6\lbrace6\rbrace6$$ in BEAF, $$6\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow6$$ in arrow notation, or 6 octated to 6.[1]. The term was coined by Aarex Tiaokhiao. This is the sixth Ackermann number.

Googology Wiki user Hyp cos calls this number a trienhex, and it's equal to s(6,6,6), s(6,2,7), s(6,6,1,2), s(6,1,1,3), or s(6,1,1,1,2) in strong array notation.[2]

## Etymology

The name of this number is based on Greek prefixes tri- (three) and hexa- (six), meaning that there are 3 6's in the array.

## Approximations

Notation Approximation
Arrow notation $$6\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow6$$ (exact)
BEAF $$\{6,6,6\}$$ (exact)
Hyper-E notation $$\textrm E[6]1\#1\#1\#1\#1\#6$$ (exact)
$$\approx\textrm E4.67\#1\#1\#1\#1\#6$$ (base 10 approximation)
Chained arrow notation $$6\rightarrow6\rightarrow6$$ (exact)
Hyperfactorial array notation $$6!5$$
Fast-growing hierarchy $$f_7(5)$$
Hardy hierarchy $$H_{\omega^7}(5)$$
Slow-growing hierarchy $$g_{\varphi(5,0)}(6)$$

## 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) · 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