iconoclasm, iconoscope, idealist, identical, idolatry, illegible, illiterate, illogical, illuminate, illusionist, illusory, illustrative, illustrious, illuvial, imaginal, immaculate, immediate, immensity, immiscible, immobilize, immoderate, immortalize, immovable, immunity, immutable, impalpable, imparity, impartable, impassable, impeccable, impediment, impenitent, imperative, imperator, imperial, imperious, impermanent, impersonal, impersonate, impertinent, impervious, impetuous, implacable, implausible, importunate, impossible, impoverish, impressible, imprimatur, improbable, improbity, improvident, impuissance, impunity, impurity, imputable, imputative, inaccurate, inactivate, inadequate, inanimate, inanity, inappetence, inapposite, inaptitude, inaugurate, incapable, incapsulate, incarcerate, incarnadine, incertitude, incestuous, incinerate, inclinable, incogitate, incompetent, incongruent, inconsequent, inconsonant, incontinent, incorporate, incredible, incredulous, incriminate, inculpable, incumbency, incurable, incurious, indebtedness, indecency, indefinite, indelible, indelicate, indemnify, indicative, indifferent, indigenous, induplicate, indusium, industrial, inebriate, inedible, ineffable, inelegant, ineloquent, ineptitude, inequity, infallible, infanticide, infatuate, infeasible, inferior, infinity, infirmary, inflammable, inflexible, informative, infrangible, infuriate, infusible, ingenious, ingenuous, inglorious, ingratitude, ingredient, ingurgitate, inhabitant, inheritance, inhibitor, iniquitous, initiate, injurious, innocuous, innominate, inoculate, inodorous, inordinate, inosculate, inquietude, inquisitive, inquisitor, insalivate, insanity, insatiable, insatiate, inscrutable, insecticide, insectivore, inseminate, insensible, insensitive, insentient, insidious, insignia, insinuate, insipience, insolvency, insouciant, inspectorate, insurancy, insurgency, intangible, integrity, integument, intelligent, intemperate, intenerate, intensify, intentional, intercolate, interior, internalize, interpolate, interrogate, intestinal, intolerant, intoxicate, intuitive, invaginate, invalidate, invariant, invertebrate, investigate, investiture, inveterate, invidious, invigorate, invincible, inviolate, invisible, ionosphere, iridium, irradiate, irrational, irregular, irrelative, irresolute, irreverent, isochronize, isochroous, isogamy, isomerous, isometry, isosceles, isostasy, and itinerant

They are four-syllable words with initial i.

In four syllable words --from aluminum to zirconium, anatomy to zoology, agronomist to zymologist -- the accent feels most comfortable on the second syllable.

ichthyosaur, ideogram, idiocy, ideolect, ignominy, implicative, incubator, indicator, infrastructure, inhalator, inspirator, integrable, interesting, interloper, intimacy, inventory, irritable, isolable, issuable, and iterative.

wenty exceptions would not be so bad -- if that were all; however, 118 four-syllable i-words are accented on the third syllable. Of those, 52 are acted on by an invisible 'ionic' force which draws the accent back to the third slot...

illustration, imbrication, imitation, imperfection, implication, importation, imposition, imprecation, imputation, inanition, inattention, incantation, incarnation, inclination, incognito, indigestion, indignation, indiscretion, inflammation, information, inhibition, innovation, innutrition, inquisition, insulation, inspiration, installation, institution, insufflation, insulation, insurrection, integration, intellection, interdiction, interjection, intermission, intersection, intersession, intervention, introduction, introjection, intromission, introspection, introversion, intuition, inundation, invitation, invocation, involution, irrigation, irritation, and isolation.

interceptor, intercostal, intercurrent, interdental, interference, interfertile, interlining, interlunar, intermarry, intermixture, internecine, interpleader, interregnum, interrupter, interstitial, intertexture, intertidal, intertribal, and interurban

intercolate, interior, internalize, interpolate, and interrogate

interesting and interloper.

interconnect and interrelate.

isoclinal, isogamete, isohyet, isometric, isooctane, isoseismic, isomotic, isothermal, isotonic, and isotropic

isochronize, isochroous, isogamy, isomerous, isometry, isosceles, and isostasy.

ichthyornis, ichthyorsis, idiotic, impetigo, inadvertent, inattentive, incandescent, incidental, incoherence, incompliant, inconclusive, inconsistent, indecisive, indecorum, independent, indication, inefficient, inelastic, inexpensive, inexplicit, inferential, influential, influenza, inharmonic, injudicious, innuendo, inobservance, inobtrusive, inoffensive, inofficious, inorganic, instrumental, insubstantial, insufficient, involucre, iridescent, and irresponsive.

indicator, indicative, and indication

In addition to...

interconnect and interrelate

inopportune.

That, in my book, deserves to be called igNOMiny.

ignominy noun Dishonor; infamy {Return}