Words pronounced with stress patterns like in "politics", "lunatics", etc.?

Most words with the suffix -ic are stressed on the immediately preceding syllable (the penult), and this rule is apparently still fairly productive for newly created words (although as far as I know, -ic itself is not especially productive as a suffix for making new adjectives).

But there are some exceptions to this pronunciation rule: some -ic words have (or can have) antepenult stress.

List of words suffixed with -ic with antepenult stress

English Word-Formation, by Laurie Bauer, cites Archibald A. Hill's 1974 article Word Stress and the Suffix -ic as giving the following list of words ending in the suffix -ic that are optionally or obligatorily pronounced with stress on the third-to-last syllable:

agaric      catholic    extuberic  oghamic    
Arabic      chivalric   heretic    phylacteric
arithmetic  choleric    lunatic    politic 
arsenic     climacteric niccolic   rhetoric
cadaveric   dominic     nickelic   theoric

In addition to these, I found a few other words that are sometimes pronounced in present-day English with the stress on the third-to-last syllable:

ichthyic, which is pronounced /ˈɪkθɪɪk/ or /ˈɪkθiɪk/
cholesteric, for which some dictionaries list a variant pronunciation /kəˈlɛstərɪk/ (see the American Heritage Dictionary and Merriam Webster)
phosphoric (Merriam-Webster)
plethoric, for which Merriam-Webster (along with the AHD) lists the variant pronunciation ˈple-thə-rik in addition to pronunciations with stress on the penultimate syllable
caloric (maybe): Collins gives ˈkælərɪk as one of the British pronunciations, and Oxford Dictionaries gives /ˈkalərɪk/ (which is equivalent). But it is a very uncommon word, and both of these dictionaries also list a pronunciation with stress on the penultimate syllable.
cherubic, which some people apparently pronounce with first-syllable stress (but the only dictionary I've been able to find that lists this pronunciation variant is Merriam-Webster)
toluic, in "toluic acid", which Merriam-Webster says can use the pronunciation ˈtälyəwik; that is, /ˈtɑljəwɪk/. Dictionary.com also lists this pronunciation. The pronunciation with initial stress seems to be modeled after the stress of the related word "toluene"
geyseric (maybe): In Correct English, Volumes 20-21, edited by Josephine Turck Baker, I found the "correct" pronunciation of the rare word geyseric ("Pertaining to a geyser") notated as "gai′ser-ik", which in this context indicates stress on the first syllable. However, this might just be an error. In any case, it is a very uncommon word.

Walker's Pronouncing Dictionary of the English Language, edited by Francis R. Sowerby, from 1862, lists some of the above words and also the following additional words, which are mainly not exceptions any more in modern speech:

ephemeric (not really in modern use)
empiric (stressed on penult nowadays)
splenetic (stressed on penult nowadays; Oxford English Dictionary says "Metrical examples show that down to the beginning of the 19th cent. the stress was on the first syllable, as given by Bailey, Johnson, and early 19th cent. Dicts.")
“perhaps” phlegmatic (“which, though more frequently heard with the accent on the antepenultimate syllable, ought if possible, to be reduced to regularity"; this wish was evidently granted as modern dictionaries all place the stress on the penult)
two words which don't actually have the suffix -ic, but just happen to end in the letters "ic": turmeric, bishopric (“better written bishoprick”)

The most frequent

In terms of frequency, the most common by far of the -ic words pronounced with stress on the antepenult syllable are politics (the adjective politic is not so common), Catholic/catholic, Arabic, rhetoric and arithmetic (the noun, not the adjective). Arsenic, lunatic, and heretic are also somewhat common. I would say that for the other words in the list, it's not really worthwhile to practice their pronunciations in order to try to memorize them, unless it's a word that you already knew and used before reading this post.

Is there any explanation for these exceptions? It's not clear.

Some of these words are common, but others are quite rare. Some are nouns, some are adjectives, and some can be used as both. Bauer does includes some theoretical discussion (which you can find by following the link), but doesn't reach a firm conclusion about why these words are exceptions.

The abstract of Hill's article says that

All but one of the exceptions are three-syllable words in which the middle syllable has a liquid or a nasal, capable of becoming syllabic under lack of stress. When this happens, the syllable to which the suffix has been added can be lost, as in such forms as earl cholryke, arsnike and the like. The one form not so explainable is arithmetic, in which the medieval folk etymology, ars metric is obviously influential.

I can attest that I do have possible elision of the middle syllable in Catholic/catholic (to "cath'lic") in my own pronunciation. This elided form is well-attested in dictionaries (The Free Dictionary by Farlex, Merriam Webster). Of course, this isn't categorical evidence that the vowel is unstressed because it can be elided; the relationship might be the reverse, that it can be elided because it is unstressed. I can't elide the vowel in most of the other words, but this may be something that has changed over time.

The supposed connection between antepenult stress in an -ic word and the presence of a resonant consonant is interesting, but I find it hard to evaluate because resonants are relatively common word-medial consonants anyway, so it seems to me that their occurence in these words might be partly a coincidence. If there is a real connection between the presence of a resononant in the coda or onset of the penult syllable and lack of penult stress in an -ic word, a possible comparison might be to the word impoverish which is stressed on the third-to-last syllable even though words ending in the verb suffix -ish are usually stressed on the second-to-last syllable (compare abolish, astonish, establish, relinquish, accomplish, distinguish; that said, prefixation might also be relevant to the stress patterns of these verbs).

Bauer describes the penult-stress rule as productive for newly coined words with the suffix -ic. However, there are degrees of productivity, and my own intuition as a native speaker is that the rule isn't completely automatic: some native speakers might be unsure in some cases, perhaps especially when adding the suffix triggers a stress shift compared to the original word, and/or when the middle syllable starts or ends with a resonant like /r/ (as suggested by Hill's examples).

For example, the adjective glyceric, which is derived from the noun glycerin(e) /ˈglɪsərɪn, ˈglɪsəˌriːn, ˌglɪsəˈriːn/ or glycerol /⁠ˈglɪsərɒl, ˈglɪsərɔːl/, is normally and normatively pronounced /ɡlɪˈsɛrɪk/, but you can find examples of people who actually pronounce it /ˈɡlɪsərɪk/ (Howjsay, and also listed as a pronunciation variant at dictionary.com). The word mesmeric is only listed by dictionaries as having the stress on the second syllable, but in fact I only just learned this while researching your question; prior to this, I mentally read it with a stress on the first syllable.

-ical: no important exceptions

As far as I can tell, there are no exceptions to the rule that words ending in the suffix -ical receive stress on the preceding syllable. This applies even to words like political, rhetorical and arithmetical, which have a stress shift relative to politic, rhetoric and arithmetic.

cervical and umbilical may have either antepenult or penult stress

There are at least two words that can be pronounced differently that end in the letters "ical", but they don't actually have the suffix -ical.

Etymologically, the word cervical is composed of cervic- (the stem of the Latin word cervix) + the suffix -al. In Latin, the "i" in the stem cervic- was long ("cervīc"), so some people pronounce the "i" in the English adjective cervical as a stressed English "long i" sound, resulting in the overall pronunciation /sərˈvaɪ.kəl/ with a stressed penult. For similar reasons, the adjective umbilical, from Latin umbilīc- (the stem of umbilīcus), is sometimes pronounced with penult stress as /ʌm.bɪˈlaɪ.kəl/. However, it seems to be most common to put stress on the antepenult for both of these words.

Also, antepenult stress is the only option in modern English (as far as I know) for some other words with similar etymology, such as radical (from Latin rādīc-, the stem of rādīx "root") and the rare word amical (from Latin amīc-, the stem of amīcus "friend") and its more common derivative inimical (from Latin inimīcus "enemy"). (Some old sources such as Walker 1791 mention that a pronunciation of inimical with the stress on the penult syllable was once in use.)

I found some interesting information about vowel length before -ic while I was doing research for this answer, so I posted it under a new question: Which words have a long vowel before the suffix -ic?