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The 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.
Trihex Integrated

Trihex visualized using iterated power towers.

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 Edit

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.

ApproximationsEdit

Notation Approximation
Up-arrow notation \(6\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow6\) (exact)
BEAF \(\{6,6,6\}\) (exact)
Hyper-E notation \(E(6)1\#1\#1\#1\#1\#6\) (exact)
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 Edit

  1. Tiaokhiao, AarexAarex's Array Notation. Retrieved December 2013.
  2. Numbers from linear array notation | Steps Toward Infinity!

See also Edit

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

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