What is the adjective for something which has vertices?

Question

I am looking for a word which describes an object which has vertices. It will be applied in the statement "Think Outside of the Eight ____ Regular Hexahedron," which is a play on words of the common phrase, "Think Outside of the Box."

I am struggling to find the proper adjective. So far, I have scoured the web. The closest word to "vertex" that I could find would be "index." When describing an object which has indices, the word "indexed" is used. Because of this, I imagine that the proper word would be "vertexed" as in "Think Outside of the Eight Vertexed Regular Hexahedron." However, I am still unsure.

Your help on the subject would be greatly appreciated! :)

Answer 1

You could try 'eight-cornered'.

Answer 2

Pointed

Usually you would say <number>-pointed with a hyphen, as in Eight-Pointed rather than Eight Pointed. I wasn't able to find this usage in the dictionary pages for "pointed" itself, but plenty of adjacent concepts mention it, for example...

1. (occult) A seven-pointed star with the construction lines retained.

https://en.wiktionary.org/wiki/heptangle

1. A blue six-pointed star...

https://en.wiktionary.org/wiki/Star_of_Life#Proper_noun

Answer 3

Keep in mind that index is both a noun and a verb, and indexed is the verb's past participle. Vertex is only a noun and has no such form, so I don't think you'll have much luck finding an appropriate form. Tipped, spired, and cornered are all possibilities, but my favorite is Eight-Pointed. Alternatively, I think Twelve-Edged sounds much more natural and still keeps the "outside the box" feel you're looking for.

Answer 4

Many stranger things have happened than turning nouns into verbs or adjectives. In fact, several words have come into existence because of just that.

The example sentence in the question looks like a slogan or title, and it's also an admitted play on words anyway.

Even if it's not strictly correct, within the context of something appropriately made up, I see nothing really wrong with the following:

Think Outside of the Eight Vertexed Regular Hexahedron

I don't think anybody could fail to understand the meaning. I wouldn't use it in any formal writing, but it might still be suitable in an informal context.

In fact, if you're trying to think outside the box anyway, don't limit yourself to making up an adjective (or verb?) that follows standard rules of syntax. In fact, it could be even better play on words …

Answer 5

According to WolframMathWorld, there is is only one regular hexahedron: the cube -- which is what you are calling "the box" in your question. There is no need for you to say anything other than "Think Outside the Regular Hexahedron."

Aside: All seven of the topologically distinct convex hexahedra have six faces by definition, but the number of vertices varies from six to eight.

Edit: We have "two faced" for two faces (e.g., two-faced person rather than two-face person) and "two edged" for two edges (e.g., two-edged sword versus two-edge sword), which indicates, for consistency's sake, the appropriate terms for n faces is "n faced" and n edges is "n edged". We also have "n pointed" for stars with n points. This suggests that the adjective you should use is "n vertexed", i.e., having eight vertices. So you could say, "Think Outside of the Eight-Vertexed Regular Hexahedron." However, as I indicated above, there is only one regular hexahedron, so "eight-vertexed" is superfluous.