A creature which walks on two legs can be referred to as biped; bi- meaning two.
A creature which walks on four legs can be referred to as quadruped; quad- meaning four.
What is the corresponding word for a six-legged creature?
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Hexapod (n., plural hexapods):
- Any organism or being with six legs.
(The Free Dictionary)
Hexapod (n.) etymology:
- "six-footed insect," 1660s, from Modern Latin hexapod-, stem of hexapodus, from Greek hex "six" (see six) + Greek pod-, stem of pous "foot" (from PIE root *ped- "foot"). Greek hexapous (adj.) was used only with reference to poetic meter. As an adjective from 1856.
Well, people balk at the risky-sounding sexaped, so you need to switch to Greek and use hexapod. Doing the same for 4- and 2-legged creatures would result in a tetrapod and a dipod. Problem with those are that they are reminiscent of a tripod, a clearly inanimate object.
All those foreign language terms come with associations reducing the applicability of the originally rather generic meaning.
Why not switch back to English and use "six-legged"? Works for insects (which is Latin for grooved beasts) as well as furniture.
I think requiring a single word for this concept is a bit unnecessary. (As user256320 says, you can just use "six-legged" or "six-footed"). But setting that aside, it's a bit tricky to say what "the" corresponding word is.
I am not a Classics expert, so some of what I say in this answer may be incorrect. If you care about forming a word in accordance with Latin/Greek precedent, probably it's best to ask the experts at the Latin Stack Exchange, or even to ask someone outside of the Stack Exchange network (gasp!) whose judgement you trust.
If you don't care about that, you can choose between any of "hexapod," "sexapod", "hexaped", "sexaped", "sexiped", "sextuped", etc. based on whatever criteria you do care about—if you want more help with that here, it would help to make it explicit what those criteria are.
(JEL in a comment references an entry in Webster's 1828 arguing for "hexaped" on the basis of uniformity with "quadruped" and "centiped". That's fine, but there's no inherent reason why anyone has to care about uniformity. Some people have an aversion to compounds that blend Latin and Greek elements, and might reject "hexaped" for this reason.)
My own preference would roughly be as follows, from my favored to least favored options: hexapod, hexaped/sexiped, sextuped, other variants.
As other answers and comments have pointed out, the word "hexapod" from Greek is the most common single word for something with six legs. I think Josh's answer is therefore quite satisfactory. Many people think frequency of usage is a good criterion for word choice.
We have other "-pod" words from Greek: the most common are tripod and tetrapod. These are based on Greek compounds ending in pous, the Greek word for "foot". There are also compounds where the initial element is not from a numeral like arthropod and gastropod. Some other words that ultimately come from Greek pous, but have developed to end in different ways in present-day English are octopus and polyp, and the plural antipodes.
From Latin, we have biped and quadruped. These are based on Latin compounds ending in pes, the Latin word for "foot". With slightly different spelling and pronunciation of the second element, we have centipede and millipede. (Centiped and milliped do exist as less common variants: someone who values consistency more than following common usage should perhaps consider choosing to use these forms.)
As far as I know, neither set of words exists in a generally-agreed-upon complete series of words for animals with n numbers of legs. Each of these words has its own history leading to its present-day use and understood meaning. For example, tripod is usually used to refer to inanimate objects (as few living organisms have three legs), while tetrapod is used in biology to refer to a specific group of animals, not all of which have four legs (humans and birds are biological tetrapods). Although the prefix milli- comes from the Latin word for "thousand," the animals we call millipedes have fewer than a thousand legs.
One thing that I have read is that compounding was not as common or productive in Classical Latin as it was in Classical Greek. Latin compounds are often somewhat artificial and belong to a learned register of the language; or they are just two separate words written together, like benefacio = bene facio "do good (literally "do well"). To me, this suggests that it's a more "risky" matter to coin words based on Latin than it is to make new words based on Greek. But that's just how I feel about it.
As I mentioned above, some people like to avoid forming or using compound words in English that have been made by combining Latin and Greek elements. Of course, many of these are too well-established to avoid, like television, but it's a matter of opinion whether that fact renders the whole endeavor pointless. See e.g. Is there a reason to use "mono" over "uni"?, Prefixes milli- and cent- used for years.
In Latin, the elements of a compound are usually "connected" with the vowel i, for some complicated historical reasons that I am not qualified to explain (but in brief, my understanding is that regular sound changes and analogy both played a role). This however is often not present when the second element of the compound starts with a vowel.
Another complication: sometimes u was used in place of i when the following consonant had a labial place of articulation, like b or p. This explains the u in the combining form quadru-, a variant of quadri- that is found in present-day English words like quadruped and quadruple. But the use of u vs. i doesn't seem to be particularly regular, as we also have centipede and millipede mentioned above, and quadripartite (which does apparently have a variant quadrupartite).
The Latin word for "six" was sex.
A search of the Perseus Digital Library turned up no compound words in Latin with "sexi-" as a prefix.
However, the Oxford English Dictionary (OED) does have an entry for sexi- as an English prefix, and this entry mentions the form "sexiped". It says
< classical Latin sex six (see sex- comb. form) + -i- connective, perhaps after quadri- comb. form, septi- comb. form1, etc. Compare sex- comb. form, sexti- comb. form, and also hexa- comb. form. Formations are found from the first half of the 19th cent. (compare sexiped n. ).
Some formations have parallels in sex- comb. form, and some have parallels in hexa- comb. form.
Although the prefix precedes a labial consonant in the word "sexiped", for some reason the "i" doesn't seem to mutate to "u" as in quadruped. I don't know if there is any theoretical way to rule out sexuped as a possibility.
The OED entry quoted above references two other similar prefixes, sex- (with no linking vowel) and sexti- (from sextus).
"Sexped" does in fact seem to have been used at leat once, in Systema Vegetabilium, but it is certainly extremely rare.
Sexti- is apparently derived from the Latin word for "sixth", sextus. Although it doesn't make much sense to me to use an ordinal number as the base of a word meaning "six-legged", the meaning of sexti- seems to have broadened compared to its origin, as the OED says it is "Attested in a small number of formations of the 16th and 17th centuries [...] forming adjectives and nouns with the sense 'having six, sixfold'". The OED's examples are sextipartite (divided into six parts), sextisection (division into six parts), sextipartition. It is also present in the variant form sextu- in the word sextuple, and the less common sextuplex.
While I haven't been able to find much evidence indicating that "sextiped" is used as a word meaning "having six legs", "sextuped" does seem to have a small but definite amount of use, judging from Google results. (I would guess that people are going on the analogy quadruple : sextuple :: quadruped : "sextuped": in fact, I see a comment by Eric Duminil made that analogy already.)
For some reason, many people seem to have the intuition that a prefix sexa- exists corresponding to the number "six". I somewhat suspect that this is simply a confusion of Latin sex and Greek hexa-, but it's possible that there is more to it. I haven't able to find any good evidence of a Latin origin for sexa- as a prefix, though.
There are Latin words starting with starting with "sexa", but as far as I can tell,they are all either compounds of "sex-" plus a word starting with "a" (as in "sexangulus"), or seem to be composed of "sex-" plus a suffix starting with "a" (as in the word sexaginta "sixty"—compare quadraginta "forty", or sexatrus "the sixth day after the Ides"—compare quinquatrus, decimatrus, septimatrus, triatrus). So, I would say that I don't know of any convincing evidence demonstrating that "sexa-" was used in Latin as a combining suffix of the same type as quadri-/quadru- or centi-.
A Wikipedia article asserts that "sexa-" is one of the "Latin" "number prefixes in English", but it's not clear what it means by this and that specific piece of information has no citation (the page as a whole cites the OED, Carl Darling Buck's Comparative Grammar of Greek and Latin, and Sihler's New Comparative Grammar of Greek and Latin, so maybe one of these sources has it, or maybe not).
Also relevant: the supposedly Latinate form "sexadecimal" as an equivalent to "hexadecimal", mentioned in the linked answer and disputed by Gilles' comment below ("but Latin would be “sedecim-”, not “sexadecim-”").
The OED does not have an entry for "sexa-" nor the word "sexaped". That said, a word doesn't have to be in the OED to be used. As I said, it's really a matter of opinion—and if you want an educated opinion about which word is most "correct", you'd have to ask someone with an education that's relevant to whatever your idea of "correct" is.