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It comes from Greek:

"dodeca-" is a transliteration (writing using similar sounding letters in the Latin alphabet) of Greek for 12 - δώδεκα

"-gon" comes from the Greek word γωνία (gonia) meaning corner (or the related word γωνιών (gonion) meaning angle).

So a dodecagon is literally a twelve-cornered or twelve-angled shape, but we tend to count sides rather than vertices and so call it a twelve-sided shape.

I guess the reason that Greek is used to name shapes is that Geometry was first studied by the Greeks.

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It comes from Greek:

"dodeca-" is a transliteration (writing using similar sounding letters in the Latin alphabet) of Greek for 12 - δώδεκα

"-gon" comes from the Greek word γωνία (gonia) meaning corner (or the related word γωνιών (gonion) meaning angle).

So a dodecagon is literally a twelve-cornered or twelve-angled shape, but we tend to count sides rather than vertices and so call it a twelve-sided shape.

I guess the reason that Greek is used to name shapes is that Geometry was first studied by the Greeks.

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-ion means process or act of in medical terminology, as in other word formations. So the process of digesting is digestion, the act of respiring is respiration, and whe we masticate, the act is mastication.
The word part -ion in medical terms means "craniometric point" as in gonion or a body point as in acromion. In common terms it can mean "condition of, result of, act of, process of, state of".
The abbreviation ion stands for several things. One of the things it stands for is Inferior Esophageal Nerve. Another item that ion stands for is Ionic Self-Diffusion Coefficient D.

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Lots!

Action

Adagio

Aiolis

Amnion

Amnios

Anions

Ariose

Ariosi

Arioso

Audios

Avions

Axioms

Axions

Bagnio

Barrio

Basion

Biogas

Biogen

Biomes

Bionic

Bionts

Biopic

Biopsy

Biotas

Biotic

Biotin

Briony

Bunion

Camion

Cardio

Cation

Curios

Daimio

Danios

Diobol

Diodes

Dioecy

Dioxan

Dioxid

Dioxin

Durion

Ethion

Fanion

Fiords

Folios

Fugios

Fusion

Gabion

Galiot

Glioma

Gonion

Griots

Havior

Helios

Heriot

Idiocy

Idioms

Idiots

Inions

Iodate

Iodide

Iodids

Iodine

Iodins

Iodise

Iodism

Iodize

Iodous

Iolite

Ionics

Ionise

Ionium

Ionize

Ionone

Junior

Kation

Kiosks

Legion

Lesion

Logion

Lotion

Manioc

Minion

Mioses

Miosis

Miotic

Morion

Motion

Nasion

Nation

Niobic

Notion

Nuncio

Odious

Onions

Oniony

Opioid

Option

Oriole

Otiose

Patios

Pavior

Period

Pernio

Pinion

Piolet

Pionic

Polios

Potion

Prions

Priors

Priory

Radios

Ration

Ratios

Region

Riojas

Rioted

Rioter

Ronion

Savior

Scions

Senior

Solion

Studio

Talion

Thiols

Triode

Triols

Triose

Turion

Unions

Vibrio

Violas

Violet

Violin

Virion

Vision

Wanion

Adios

Agios

Aioli

Amnio

Anion

Audio

Avion

Axiom

Axion

Biogs

Biome

Biont

Biota

Brios

Cions

Curio

Danio

Diode

Diols

Fiord

Folio

Fugio

Griot

Helio

Idiom

Idiot

Inion

Iodic

Iodid

Iodin

Ionic

Iotas

Kiosk

Lions

Olios

Onion

Patio

Pions

Pious

Polio

Prion

Prior

Radio

Ratio

Rioja

Riots

Scion

Thiol

Triol

Trios

Union

Viola

Viols

Agio

Biog

Bios

Brio

Cion

Diol

Ions

Iota

Lion

Olio

Pion

Riot

Thio

Trio

Viol

Bio

Ion

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4-letter words

agin, agio, agly, agon, ahoy, alit, ally, alto, anil, anon, anti, ayin, gain, gait, gall, gaol, ghat, gill, gilt, glia, gnat, goal, goat, goon, hail, hall, halo, halt, hang, hant, hila, hili, hill, hilt, hint, holt, holy, hong, hoot, hoya, hyla, ilia, illy, inia, inly, inti, into, iota, lain, lang, lath, lati, lilt, lily, ling, linn, lino, lint, liny, lion, loan, logo, logy, loin, long, loon, loot, lota, loth, loti, nail, naoi, nigh, nill, noil, nolo, nona, noon, nota, oath, ohia, oily, olio, olla, only, onto, tail, tain, tali, tall, tang, than, thin, thio, till, ting, tiny, toga, toil, tola, toll, tong, tony, tool, toon, toyo, yagi, yang, yill, yoga, yogh, yogi, yoni

5-letter words

agony, aioli, algin, align, allot, alloy, aloin, along, altho, anion, annoy, atoll, atony, gaily, gally, ghyll, giant, gilly, ginny, glial, glint, gloat, golly, gonia, goony, hallo, hillo, hilly, hinny, hoagy, hogan, holla, hollo, holly, honan, hooly, hooty, hotly, hying, igloo, ilial, ingot, inion, inlay, laigh, laith, laity, lathi, lathy, liang, ligan, light, linga, lingo, lingy, linin, linty, litai, litho, llano, loath, logan, logia, logoi, loony, lotah, loyal, lying, nanny, night, nihil, ninny, ninon, ninth, niton, noily, nonyl, notal, nylon, ohing, ology, onion, tally, talon, tango, tangy, thill, thing, thiol, thong, tigon, tinny, tolan, tolyl, tonal, tonga, toyon, tying, yahoo, yogin

6-letter words

ailing, alight, aliyot, anilin, anoint, anting, gainly, galiot, gallon, galoot, gitano, gonion, haling, halloo, hallot, hating, haying, hilloa, holily, holing, holloa, holloo, honing, hyalin, inning, lagoon, latigo, latino, laying, lignin, lining, lintol, litany, lithia, logily, logion, longan, longly, looing, lotion, nation, nighty, nilgai, nongay, noting, notion, oilily, oiling, oohing, oolith, oology, oolong, otalgy, tahini, talion, tangly, tannin, thalli, thinly, tholoi, tiglon, tiling, tingly, tinily, tining, toling, toning, toying, tyning, yogini

7-letter words

agility, alining, allying, anility, anthill, antilog, antlion, atoning, galliot, galloon, galloot, glonoin, hailing, haloing, halting, hanting, hilling, hilting, hinting, hooting, inanity, initial, intagli, laithly, lanolin, lathing, lightly, lilting, loaning, loathly, looting, nailing, nightly, nilghai, nilling, ninthly, nitinol, nonagon, nooning, nothing, nylghai, oogonia, otology, tailing, tallyho, tanning, thionin, thionyl, tholing, tilling, tinnily, tinning, toiling, tolling, tonally, tooling

8-letter words

alloying, annoying, antilogy, anything, gnathion, halloing, hilloing, hinnying, hollaing, holloing, hooligan, ignition, illation, inhaling, inlaying, intaglio, intoning, ligation, lithoing, loathing, nihility, nontonal, notional, oinology, ontology, oogonial, tallying, thinning

9-letter words

anointing, anthology, hallooing, haltingly, hilloaing, holloaing, hollooing, inanition, initially, lithology, nonillion

10-letter words

noninitial, notionally, tallyhoing

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4-letter words

acme, acne, aeon, agin, agio, agon, amen, amie, amin, anon, ante, anti, atom, cage, cain, came, cane, cant, cate, cent, ciao, cine, cion, cite, coat, coin, coma, come, cone, coni, conn, coon, coot, cote, emic, emit, etic, etna, gaen, gain, gait, game, gane, gate, gent, geta, gien, gnat, goat, gone, goon, icon, inia, inti, into, iota, item, mace, mage, magi, main, mane, mano, mate, matt, mean, meat, meno, meta, mica, mice, mien, mina, mine, mini, mint, mite, mitt, moan, moat, mono, moon, moot, mote, mott, name, naoi, neat, nema, neon, nett, nice, nine, noma, nome, nona, none, noon, nota, note, ogam, omen, omit, once, onto, otic, otto, tace, taco, tact, tain, tame, tang, tate, team, teat, tent, time, tine, ting, tint, titi, toea, toga, toit, tome, tone, tong, toom, toon, toot, tote

5-letter words

acing, acini, actin, agent, agone, ament, amice, amigo, amine, amino, amnic, among, ancon, anent, anime, animi, anion, antic, atone, attic, cameo, canoe, canon, canto, cento, coati, cogon, coign, comae, comet, comte, conga, conge, congo, conin, conte, conto, cotan, cotta, enact, entia, gamic, gamin, gemot, genic, genii, genoa, genom, giant, gnome, gonia, icing, image, imago, imine, imino, inane, incog, ingot, inion, ionic, macon, magic, magot, mange, mango, manic, matin, matte, meant, menta, minae, mince, mongo, monie, monte, motet, motte, motto, niton, nomen, nomoi, nonce, nonet, oaten, ocean, octan, octet, omega, onion, ontic, tacet, tacit, taint, tango, tanto, tecta, tenia, tenon, tigon, tinct, tinea, tinge, titan, togae, toman, tonga, tonic, tonne, totem

6-letter words

acetin, acting, action, aeonic, agonic, aiming, aminic, amnion, ancone, anemic, anoint, anomic, anomie, anting, atomic, atonic, camion, canine, caning, cannie, cannot, canton, cation, cattie, cinema, citing, cogent, cogito, coigne, comate, coming, congii, conine, coning, cooing, cootie, coting, cottae, cotton, eating, enatic, encina, enigma, eonian, etamin, gamine, gannet, gitano, gnomic, gnomon, gonion, goonie, gotten, iceman, ignite, incage, incant, incite, income, ingate, inmate, innate, intact, intent, intima, intime, intine, intone, ionone, macing, magnet, manioc, manito, mantic, mating, mattin, meting, mignon, mining, minion, miotic, mitten, mongoe, mooing, motion, naming, nation, niacin, nocent, noetic, nomina, nonage, noncom, nonego, notate, notice, noting, notion, octane, octant, omenta, oomiac, otitic, tamein, taming, tannic, tenant, tieing, timing, tining, tinman, tinmen, titian, titman, titmen, toeing, togate, tomato, tomcat, toning, toting

7-letter words

aconite, actinon, agnomen, amniote, amotion, ancient, anionic, anteing, antigen, atoning, canting, catmint, catting, centimo, coagent, coaming, coating, cognate, coinage, coining, coition, comitia, coniine, connate, connote, contain, contemn, content, coontie, cottage, emoting, emotion, enation, encomia, gametic, genomic, gentian, imagine, imitate, intimae, ionogen, iteming, magneto, mannite, matting, meaning, megaton, meiotic, mention, mincing, mintage, minting, mitogen, mitotic, moaning, moating, montage, montane, mooning, mooting, negaton, nematic, netting, nicotin, nictate, nongame, nonmeat, octagon, omening, ottoman, taction, tangent, teaming, tegmina, tenting, tetanic, tinting, titanic, titmice, toiting, tomenta, tonemic, tonetic, tongman, tongmen, tonnage, tontine, tooting, totemic

8-letter words

amitotic, amnionic, amniotic, cameoing, canoeing, citation, cogitate, cognomen, coinmate, conation, cotenant, emitting, enacting, enticing, gnomonic, inaction, incitant, incoming, intimate, intonate, magnetic, magneton, mannitic, menacing, mitigate, monecian, monition, monotint, negation, nicotine, nominate, nonimage, noontime, notating, notation, noticing, ointment, omitting, oncoming, taconite, tainting, tincting

9-letter words

antigenic, antinomic, cognation, cognition, cognomina, contagion, cotangent, cottoning, enigmatic, geomantic, incognita, incognito, manicotti, mentation, mitogenic, monogenic, motioning, negotiant, nictating, nonatomic

10-letter words

cogitation, gemination, gentamicin, incogitant

11-letter words

negotiation

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