On a two-dimensional Cartesian plane we can naturally subdivide the space into four quadrants at the origin. In three-dimensions, the partition into eight parts are known as octants. In four-dimensional space we have sixteen parts; what is the corresponding name for each partition?

Wikipedia has an n-dimensional name:

In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.

Even if it isn't common usage, what would the next term be for 4-dimensions (of sixteen parts)?

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    In heraldry, it's called Seize Quartiers. But that only refers to having inherited 16 coats of arms, each from an armigerous ancestor -- basically it means all 16 of one's great-great-grandparents had arms. – John Lawler Oct 30 '13 at 17:34

The Latin for sixteen is sedecim, so one could coin the term sedecimant for the 16 orthants of four-dimensional space.

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  • Could there possibly be an alternate spelling of that? Googling the word gives exactly two results, this post and another on Math SE where a comment posits the exact same thing: math.stackexchange.com/a/434503/196 – Hooked Oct 30 '13 at 17:46
  • That's because there isn't a word; it's coined specially. Nice to know that I came up with the same word as a mathematician though. – Andrew Leach Oct 30 '13 at 17:50
  • I asked since I don't know how Latin modifies the prefix, e.g. eight -> octo but eight+"sections" -> "octant", so does sixteen+"sections" still read as sedecim+"ant"? – Hooked Oct 30 '13 at 17:55
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    The -ant needs to be immediately preceded by a consonant, and sedecim conveniently provides one. If the suffix were -pant, the sequence would likely be quadrapant, octopant, sedecipant. – Andrew Leach Oct 30 '13 at 18:02

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