The greagol regiment is a series of numbers from E100#100#100 to E1#1#1#10,000 defined using Hyper-E notation (i.e. beginning from greagol and up to myria-petaxis).[1] The numbers were coined by Sbiis Saibian.
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Grangol regiment | Gigangol regiment |
List of numbers of the regiment
Name of number | Hyper-E Notation (definition) | Scientific notation (exact value) | Scientific notation (approximation) | Fast-growing hierarchy (approximation) |
---|---|---|---|---|
Greagol | E100#100#100 | \(\left.\begin{matrix}\underbrace{10^{...^{10^{100}}}} \\ \underbrace{\quad\;\; \vdots \quad\;\;} \\ \underbrace{10^{...^{10^{100}}}} \\ 100\quad 10's \end{matrix} \right \} \text{100 lower braces}\) | \(100 \uparrow\uparrow\uparrow 100\) | \(f_4(100)\) |
Googolthrex | E100#1#1#2 = E100#100#googol | \(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} 10^{100}\) | \(100 \uparrow\uparrow\uparrow 10\uparrow 100\) | \(f_4(f_2(324))\) |
Googolplexithrex | E100#2#1#2 = E100#100#googolplex | \(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} 10^{10^{100}}\) | \(100 \uparrow\uparrow\uparrow 10\uparrow 10\uparrow 100\) | \(f_4(f_2^2(324))\) |
Grangolthrex | E100#100#1#2 = E100#100#grangol | \(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}\) | \(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4(f_3(100))\) |
Grangoldexithrex | E100#100#2#2 = E100#100#grangoldex | \(\left. \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}\) | \(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4(f_3^2(100))\) |
Grangoldudexithrex | E100#100#3#2 = E100#100#grangoldudex | \(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\& & 100\quad 10's \end{matrix} \right \} \text {3 lower braces}\) | \(100 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4(f_3^3(100))\) |
Greagolthrex | E100#100#100#2 = E100#100#(E100#100#100) = E100#100#greagol | \(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {100 lower braces}\) | \(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 100\) | \(f_4^2(100)\) |
Grangolduthrex | E100#100#1#3 = E100#100#grangol#2 | \(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}\) | \(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4^2(f_3(100))\) |
Grangoldexiduthrex | E100#100#2#3 = E100#100#grangoldex#2 | \(\left. \left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \underbrace{10^{10^{...{^{10^{100}}}}}}_{\underbrace{10^{10^{...{^{10^{100}}}}}}_{100\quad 10's}}\) | \(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4^2(f_3^2(100))\) |
Grangoldudexiduthrex | E100#100#3#3 = E100#100#grangoldudex#2 | \(\left. \left.\left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\&&\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {3 lower braces}\) | \(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 10\uparrow\uparrow 100\) | \(f_4^2(f_3^3(100))\) |
Greagolduthrex | E100#100#100#3 = E100#100#(E100#100#100#2) = E100#100#greagolthrex | \(\left. \left.\left.\begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \begin{matrix} &&\underbrace{10^{10^{...{^{10^{100}}}}}}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & \underbrace{\quad \;\; \vdots \quad\;\;}\\ & &\underbrace{10^{10^{...{^{10^{100}}}}}} \\ & & 100\quad 10's \end{matrix} \right \} \text {100 lower braces}\) | \(10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10\uparrow\uparrow\uparrow 100\) | \(f_4^3(100)\) |
Name of number | Hyper-E Notation (definition) | Arrow notation (approximation) | Fast-growing hierarchy (approximation) |
---|---|---|---|
Grangoltrithrex | E100#100#1#4 = E100#100#grangol#3 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))\) | \(f_4^3(f_3(100))\) |
Grangoldexitrithrex | E100#100#2#4 = E100#100#grangoldex#3 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))\) | \(f_4^3(f_3^2(100))\) |
Grangoldudexitrithrex | E100#100#3#4 = E100#100#grangoldudex#3 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))\) | \(f_4^3(f_3^3(100))\) |
Greagoltrithrex | E100#100#100#4 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))\) | \(f_4^4(100)\) |
Grangolquadrithrex | E100#100#1#5 = E100#100#grangol#4 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101)))))\) | \(f_4^4(f_3(100))\) |
Grangoldexiquadrithrex | E100#100#2#5 = E100#100#grangoldex#4 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3))))\) | \(f_4^4(f_3^2(100))\) |
Grangoldudexiquadrithrex | E100#100#3#5 = E100#100#grangoldudex#4 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4))))\) | \(f_4^4(f_3^3(100))\) |
Greagolquadrithrex | E100#100#100#5 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101))))\) | \(f_4^5(100)\) |
Grangolquintithrex | E100#100#1#6 = E100#100#grangol#5 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^2(101))))))\) | \(f_4^5(f_3(100))\) |
Grangoldexiquintithrex | E100#100#2#6 = E100#100#grangoldex#5 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 3)))))\) | \(f_4^5(f_3^2(100))\) |
Grangoldudexiquintithrex | E100#100#3#6 = E100#100#grangoldudex#5 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 4)))))\) | \(f_4^5(f_3^3(100))\) |
Greagolquintithrex | E100#100#100#6 | \(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3(10\uparrow^3 101)))))\) | \(f_4^6(100)\) |
Greagolsextithrex | E100#100#100#7 | \(10\uparrow^4 8\) | \(f_4^7(100)\) |
Greagolseptithrex | E100#100#100#8 | \(10\uparrow^4 9\) | \(f_4^8(100)\) |
Greagoloctithrex | E100#100#100#9 | \(10\uparrow^4 10\) | \(f_4^9(100)\) |
Greagolnonithrex | E100#100#100#10 | \(10\uparrow^4 11\) | \(f_4^{10}(100)\) |
Greagoldecithrex | E100#100#100#11 | \(10\uparrow^4 12\) | \(f_4^{11}(100)\) |
Greagolthrexichime | E1000#1000#1000#2 | \(10\uparrow^3 (10\uparrow^3 (1001))\) | \(f_4^2(1000)\) |
Greagolduthrexichime | E1000#1000#1000#3 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))\) | \(f_4^2(f_3(1000))\) |
Greagoltrithrexichime | E1000#1000#1000#4 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))\) | \(f_4^3(f_3(1000))\) |
Greagolquadrithrexichime | E1000#1000#1000#5 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001)))))\) | \(f_4^4(f_3(1000))\) |
Greagolquintithrexichime | E1000#1000#1000#6 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (1001))))))\) | \(f_4^5(f_3(1000))\) |
Greagoltoll | E10,000#10,000#10,000 | \(10\uparrow^3 (10^4)\) | \(f_4(10,000)\) |
Greagolthrexitoll | E10,000#10,000#10,000#2 | \(10\uparrow^3 (10\uparrow^3 (10^4))\) | \(f_4(f_3(10,000))\) |
Greagolduthrexitoll | E10,000#10,000#10,000#3 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\) | \(f_4^2(f_3(10,000))\) |
Greagoltrithrexitoll | E10,000#10,000#10,000#4 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))\) | \(f_4^3(f_3(10,000))\) |
Greagolquadrithrexitoll | E10,000#10,000#10,000#5 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4))))\) | \(f_4^4(f_3(10,000))\) |
Greagolquintithrexitoll | E10,000#10,000#10,000#6 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^4)))))\) | \(f_4^5(f_3(10,000))\) |
Greagolgong | E100,000#100,000#100,000 | \(10\uparrow^3 (10^5)\) | \(f_4(100,000)\) |
Greagolthrexigong | E100,000#100,000#100,000#2 | \(10\uparrow^3 (10\uparrow^3 (10^5))\) | \(f_4(f_3(100,000))\) |
Greagolduthrexigong | E100,000#100,000#100,000#3 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))\) | \(f_4^2(f_3(100,000))\) |
Greagoltrithrexigong | E100,000#100,000#100,000#4 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))\) | \(f_4^3(f_3(100,000))\) |
Greagolquadrithrexigong | E100,000#100,000#100,000#5 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5)))))\) | \(f_4^4(f_3(100,000))\) |
Greagolquintithrexigong | E100,000#100,000#100,000#6 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^5))))))\) | \(f_4^5(f_3(100,000))\) |
Greagolbong | E100,000,000#100,000,000#100,000,000 | \(10\uparrow^3 (10^8)\) | \(f_4(10^8)\) |
Greagolthrexibong | E100,000,000#100,000,000#100,000,000#2 | \(10\uparrow^3 (10\uparrow^3 (10^8))\) | \(f_4(f_3(10^8))\) |
Greagolduthrexibong | E100,000,000#100,000,000#100,000,000#3 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^8)))\) | \(f_4^2(f_3(10^8))\) |
Greagolthrong | E100,000,000,000#100,000,000,000#100,000,000,000 | \(10\uparrow^3 (10^{11})\) | \(f_4(10^{11})\) |
Greagolthrexithrong | E100,000,000,000#100,000,000,000#100,000,000,000#2 | \(10\uparrow^3 (10\uparrow^3 (10^{11}))\) | \(f_4(f_3(10^{11}))\) |
Greagolduthrexithrong | E100,000,000,000#100,000,000,000#100,000,000,000#3 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{11})))\) | \(f_4^2(f_3(10^{11}))\) |
Gaggolchime | E1#1#1000 | \(10\uparrow^3 1000\) | \(f_4(1000)\) |
Gaggoltoll | E1#1#10,000 | \(10\uparrow^3 10000\) | \(f_4(10,000)\) |
Gaggolgong | E1#1#100,000 | \(10\uparrow^3 100000\) | \(f_4(100,000)\) |
Gaggolbong | E1#1#100,000,000 | \(10\uparrow^3 10^8\) | \(f_4(10^8)\) |
Gaggolthrong | E1#1#100,000,000,000 | \(10\uparrow^3 10^{11}\) | \(f_4(10^{11})\) |
Googolthrex | E100#1#1#2 = E100#1#googol | \(10\uparrow^3 10^{100}\) | \(f_4(f_2(324))\) |
Googolplexithrex | E100#2#1#2 = E100#2#googolplex | \(10\uparrow^3 10^{10^{10^{100}}}\) | \(f_4(f_2^2(324))\) |
Googoldexithrex | E100#1#2#2 = E100#1#(E100#1#2) | \(10\uparrow^3 (10\uparrow^2 (10^{100}))\) | \(f_4(f_3(f_2(324)))\) |
Greagolplex | E(E100#100#100) | \(10\uparrow (10\uparrow^3 (101))\) | \(f_2(f_4(100))\) |
Greagoldex | E100#(E100#100#100) = E100#100#101 | \(10\uparrow^2 (10\uparrow^3 (101))\) | \(f_4(101)\) |
Ecetonthrex | E303#1#1#2 = E303#1#(E303) = E303#1#centillion | \(10\uparrow^3 (10^{303})\) | \(f_4(996)\) |
Ecetonduthrex | E303#1#1#3 = E303#1#ecetonthrex | \(10\uparrow^3 (10\uparrow^3 (10^{303}))\) | \(f_4^2(996)\) |
Ecetontrithrex | E303#1#1#4 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))\) | \(f_4^3(996)\) |
Ecetonquadrithrex | E303#1#1#5 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303}))))\) | \(f_4^4(996)\) |
Ecetonquintithrex | E303#1#1#6 | \(10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10\uparrow^3 (10^{303})))))\) | \(f_4^5(996)\) |
Tria-petaxis | E1#1#1#3 = E1#1#deka-taxis | \(10\uparrow^4 3\) | \(f_4^2(10)\) |
Tetra-petaxis | E1#1#1#4 = E1#1#tria-petaxis | \(10\uparrow^4 4\) | \(f_4^3(10)\) |
Penta-petaxis | E1#1#1#5 = E1#1#tetra-petaxis | \(10\uparrow^4 5\) | \(f_4^4(10)\) |
Hexa-petaxis | E1#1#1#6 = E1#1#penta-petaxis | \(10\uparrow^4 6\) | \(f_4^5(10)\) |
Hepta-petaxis | E1#1#1#7 = E1#1#hexa-petaxis | \(10\uparrow^4 7\) | \(f_4^6(10)\) |
Octa-petaxis | E1#1#1#8 = E1#1#hepta-petaxis | \(10\uparrow^4 8\) | \(f_4^7(10)\) |
Enna-petaxis | E1#1#1#9 = E1#1#octa-petaxis | \(10\uparrow^4 9\) | \(f_4^8(10)\) |
Deka-petaxis | E1#1#1#10 = E1#1#enna-petaxis | \(10\uparrow^4 10\) | \(f_4^9(10)\) |
Hecta-petaxis | E1#1#1#100 | \(10\uparrow^4 100\) | \(f_5(99)\) |
Chilia-petaxis | E1#1#1#1000 | \(10\uparrow^4 1000\) | \(f_5(999)\) |
Myria-petaxis | E1#1#1#10,000 | \(10\uparrow^4 10000\) | \(f_5(9999)\) |
Etymology
Parts of names | Meaning |
---|---|
tria | 3 |
tetra | 4 |
penta | 5 |
hexa | 6 |
hepta | 7 |
octa | 8 |
enna | 9 |
deka | 10 |
hecta | 100 |
chilia | 1000 |
myria | 10000 |
ding | multiply the base value by 5 |
chime | multiply the base value by 10 |
bell | multiply the base value by 50 |
toll | multiply the base value by 100 |
gong | multiply the base value by 1000 |
bong | multiply the base value by \(10^6\) |
throng | multiply the base value by \(10^9\) |
gandingan | multiply the base value by \(10^{12}\) |
Sources
- ↑ Sbiis Saibian, 4.3.2 - Hyper-E Numbers
Hyper-E regiments: Guppy regiment · Grangol regiment · Greagol regiment · Gigangol regiment · Gorgegol regiment · Gulgol regiment · Gaspgol regiment · Ginorgol regiment · Gargantuul regiment · Googondol regiment
Extended Hyper-E regiments: Gugold regiment · Graatagold regiment · Greegold regiment · Grinningold regiment · Golaagold regiment · Gruelohgold regiment · Gaspgold regiment · Ginorgold regiment · Gargantuuld regiment · Googondold regiment · Gugolthra regiment · Throogol regiment · Tetroogol regiment · Pentoogol regiment · Hexoogol regiment · Heptoogol regiment · Ogdoogol regiment · Entoogol regiment · Dektoogol regiment
Cascading-E regiments: Godgahlah regiment · Gridgahlah regiment · Kubikahlah regiment · Quarticahlah regiment · Quinticahlah regiment · Sexticahlah regiment · Septicahlah regiment · Octicahlah regiment · Nonicahlah regiment · Decicahlah regiment · Godgathor regiment · Gralgathor regiment · Thraelgathor regiment · Terinngathor regiment · Pentaelgathor regiment · Hexaelgathor regiment · Heptaelgathor regiment · Octaelgathor regiment · Ennaelgathor regiment · Dekaelgathor regiment · Godtothol regiment · Godtertol regiment · Godtopol regiment · Godhathor regiment · Godheptol regiment · Godoctol regiment · Godentol regiment · Goddekathol regiment
Extended Cascading-E regiments: Tethrathoth regiment · Monster-Giant regiment · Tethriterator regiment · Tethracross regiment · Tethracubor regiment · Tethrateron regiment · Tethrapeton regiment · Tethrahexon regiment · Tethrahepton regiment · Tethra-ogdon regiment · Tethrennon regiment · Tethradekon regiment · Tethratope regiment · Pentacthulhum regiment · Pentacthulcross regiment · Pentacthulcubor regiment · Pentacthulteron regiment · Pentacthulpeton regiment · Pentacthulhexon regiment · Pentacthulhepton regiment · Pentacthul-ogdon regiment · Pentacthulennon regiment · Pentacthuldekon regiment · Pentacthultope regiment · Hexacthulhum super regiment · Heptacthulhum super regiment · Ogdacthulhum super regiment · Ennacthulhum super regiment · Dekacthulhum super regiment
Beyond...: Blasphemorgulus regiment
Redstonepillager's extensions: Extended Gridgahlah regiment · Tethratopothoth regiment · Godsgodgulus regiment · Blasphemorgulus regiment · Blasphemordeugulus regiment · Ominongulus regiment