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## Tier 0

Aarex’s Tier 0 is obvious, since it’s just the already extant names of the hypercubes up through to 5. These are, for completeness:

• $0$D – Point
• $1$D – Line Segment
• $2$D – Square
• $3$D – Cube
• $4$D – Tesseract
• $5$D – Penteract

## Tier 1

Tier 1 is slightly less obvious, but becomes more so when converting the dimensionality of the hypercube into number base 6. The units digit comes at the end of the hypercube’s name, and is based purely on the Tier 0 names (with the addition of –act, when the final digit is 0).

The sixes digit is killer-, with the multiplier placed before it based upon the Tier 0 names. For example, a $25$D hypercube would be named by first converting it to base 6, which would give ${ 41 }_{ 6 }$D. This would be named a tesserkillerline – “tesserkiller-” meaning that the sixes digit is four (“tesser-” meaning four, “-killer” meaning the sixes digit), and “-line” meaning that the units digit is one.

Another example is an $18$D hypercube. This would be converted to base 6 to give ${ 30 }_{ 6 }$D, meaning that is would be named a cuberkilleract.

The thirty-sixes (=${6}^{2}$) digit is meger-; the two-hundred-sixteens (=${6}^{3}$) digit is giger-; the ${6}^{4}$ digit is terer-; and the ${6}^{5}$ digit it peter-. These are multiplied according to the same rules as –killer.

For example, a $2967$D hypercube would first have its dimensions converted to base 6. This gives ${ 21423 }_{ 6 }$D. This would be a squarterergigertessermegersquarkillercube. The terer- term ($6^4$) is two, hence the squarterer- part. The giger- term ($6^3$) is one, so it is just -giger-. The meger- term ($6^2$) is four, hence the -tessermeger- part. The killer- ($6^1$) is two, hence the -squarkiller- part. Finally, the final digit is three, so it ends with -cube.

That’s all you need to know to name any hypercube of Tiers 0 and 1, from $0$D to ${ 6 }^{ 6 }-1$D. Congratulations!

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