Etymology
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Words related to Polish

*pel- (5)
Proto-Indo-European root meaning "to thrust, strike, drive."

It forms all or part of: anvil; appeal; catapult; compel; dispel; expel; felt (n.) "unwoven fabric matted together by rolling or beating;" filter; filtrate; impel; impulse; interpellation; interpolate; peal; pelt (v.) "to strike (with something);" polish; propel; pulsate; pulsation; pulse (n.1) "a throb, a beat;" push; rappel; repeal; repel; repousse.

It is the hypothetical source of/evidence for its existence is provided by: Greek pallein "to wield, brandish, swing," pelemizein "to shake, cause to tremble;" Latin pellere "to push, drive;" Old Church Slavonic plŭstĭ.
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polite (adj.)

late 14c., "polished, burnished" (mid-13c. as a surname), from Latin politus "refined, elegant, accomplished," literally "polished," past participle of polire "to polish, to make smooth" (see polish (v.)).

The literal sense is obsolete in English; the sense of "elegant, cultured" (of literature, arts, etc.) is from c. 1500; of persons, "refined or cultivated in speech, manner, or behavior," by 1620s. The meaning "behaving courteously, showing consideration for others" is by 1748 (implied in politely). Related: Politeness.

Polite applies to one who shows a polished civility, who has a higher training in ease and gracefulness of manners: politeness is a deeper, more comprehensive, more delicate, and perhaps more genuine thing than civility. Polite, though much abused, is becoming the standard word for the bearing of a refined and kind person toward others. [Century Dictionary, 1895]
polished (adj.)
late 14c., "made smooth;" early 15c., "elegant;" past-participle adjective from polish (v.).
pole (n.1)

"stake, staff," late Old English pal "stake, pole, post," a general Germanic borrowing (Old Frisian and Old Saxon pal "stake," Middle Dutch pael, Dutch paal, Old High German pfal, Old Norse pall) from Latin palus "a stake," from PIE *pakslo-, suffixed form of root *pag- "to fasten." Later specifically "a long, slender, tapering piece of wood."

Racing sense of "inside pole-fence surrounding a course" is from 1851; hence pole position in auto racing (1904). A ten-foot pole as a metaphoric measure of something one would not touch something (or someone) else with is by 1839, American English. The ten-foot pole was a common tool used to set stakes for fences, etc., and the phrase "Can't touch de bottom with a ten foot pole" is in the popular old minstrel show song "Camptown Races."

"I saw her eat."
"No very unnatural occurrence I should think."
"But she ate an onion!"
"Right my boy, right, never marry a woman who would touch an onion with a ten foot pole."
[The Collegian, University of Virginia, June 1839]
-ish 
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.

The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.
nail-polish (n.)

"lacquer applied to the fingernail or toenails to protect and decorate," 1881, from nail (n.) + polish (n.).

unpolished (adj.)
late 14c., from un- (1) "not" + past participle of polish (v.). In reference to style, language, etc., attested from late 15c. Less common impolished is attested from 1580s.