Trihexo

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Visualization of trihexo using exponentiation

Trihexo is equal to s(3,3,6) in strong array notation. 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).

Etymology

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.

Approximations

Notation	Approximation
Arrow notation	\(3\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow3\) (exact)
Bowers' Exploding Array Function	\(\{3,3,6\}\) (exact)
Chained arrow notation	\(3\rightarrow3\rightarrow6\) (exact)
Hyper-E notation	\(\textrm E[3]1\#1\#1\#1\#1\#3\) (exact)
Hyperfactorial array notation	\(4!5\)
Fast-growing hierarchy	\(f_7(2)\)
Hardy hierarchy	\(H_{\omega^7}(2)\)
Slow-growing hierarchy	\(g_{\varphi(5,0)}(3)\)

See also

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

4-entry series

Primitol group: primitol · primitolplex · primitolbiplex · primitoltriplex · primitolquadriplex · primibol · primibolplex · primitrol · primitrolplex · primitetol · primitetolplex · primipenol · primipenolplex
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex

5-entry series

Chainol group: chainol · chainolplex · chainolbiplex · chainoltriplex · chainolquadriplex · chainbol · chainbolplex · chaintrol · chaintrolplex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex

6-entry series

Choinol group: choinol · choinolplex · choinalbiplex · choinbol · choinbolplex · choinprimol · choinprimolplex · choinpribol · choinpribolplex · choinduprimol · choinduprimolplex · choindupribol · choindupribolplex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex