Visualization of trihexo using exponentiation

The trihexo is equal to s(3,3,6) in strong array notation.[1] The term was coined by wiki user Hyp cos. It can be represented in up-arrow notation as \(3\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow3\) (3 octated to 3).

This number is also equal to s(3,2,7) and s(3,6,1,2).


The name of this number is based on the word "tri" and "hexa" (Greek for 3 and 6), meaning a base-3 number, generated using hyper-6 operation based on exponentiation.


Notation Approximation
Up-arrow notation \(3\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow3\) (exact)
BEAF \(\{3,3,6\}\) (exact)
Hyper-E notation \(E(3)1\#1\#1\#1\#1\#3\) (exact)
Chained arrow notation \(3\rightarrow3\rightarrow6\) (exact)
Hyperfactorial array notation \(4!5\)
Fast-growing hierarchy \(f_7(2)\)
Hardy hierarchy \(H_{\omega^7}(2)\)
Slow-growing hierarchy \(g_{\varphi(5,0)}(3)\)


  1. Numbers from linear array notation | Steps Toward Infinity!

See alsoEdit

Hyp cos' linear strong array notation numbers | exAN numbers
3-entry series
Tribo group: tribo · tetbo · pentbo · hexabo
Trientri group: trientri · tettro · pentro · hextro
Trientet group: triteto · trientet · penteto · hexteto
Trienpent group: tripeno · tetpeno · trienpent · hexpeno
Trienhex group: trihexo · tethexo · penhexo · trienhex

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