|Polykrates by M. Kozlovsky (1790)|
First, Herodotus lived in the fifth century (ca. 484–ca. 425) BCE and probably sometime around the year 425 BCE wrote his magnum opus, a long account of the Greco-Persian Wars that he titled The Histories.
In it we have an account of the fate Polycrates, tyrant of Samos, who lived from ca. 538 BCE to 522 BCE at the hand of a Persian Satrap, Oroestes.
“Having killed him in a manner not fit to be told, Oroetes suspended him” (Apokteinas de min ouk axiôs apêgêsois Oroitês anestaurôse) (Herodotus Histories 3.125.3)
A “manner not fit to be told” (Greek original) suggests that the manner used to kill Polycrates was degrading and not appropriate for one of Polycrates' station, his public visage. But it also suggests that the manner of death was simply too hideous for the listeners of Herodotus’ The Histories as read out loud, and for the readers. Both are confirmed by the verbiage in 3.125.2: “After having come into Magnesia, Polycrates was horribly destroyed, and not [in a manner] worthy of him and of his high thoughts” (apikomenos de es tên Magnêsiên ho Polukratês dieftharê kakôs, oute eôutou axiôs oute tôn eôutou fronêmatôn). And the mention that Oroetes suspended him – Oroitês anestaurôse – follows immediately after the mention of his having killed him suggests that there was probably no interruption between his death and subsequent suspension, and that the manner of death probably was intended to take a long time to kill, while Polycrates was suspended. The manner of execution that best fits the bill in my opinion is impalement: not crucifixion, which was a Roman penalty, and not tying to a pole.
 Oswald Spengler, The Decline of the West, an abridged edition by Helmut Werner, English abridged edition prepared by Arthur Helps from the translation by Charles Francis Atkinson. New York: Vintage Books (Random House), 2006, p. 166 including n. 8 (color-formatting and Greek transliteration mine):
It goes without saying that we, when we turn to look into the Classical life-feeling, must find these some basic element of ethical values that is antithetical to “character” in the same way as the statue is antithetical to the fugue, Euclidean geometry to Analysis, and body to space. We find it in the Gesture. It is this that provides the necessary foundation for a spiritual static. The word that stands in the Classical vocabulary where “personality” stands in our own is prosôpon, persona--namely, role or mask. In the late Greek or Roman speech it means the public aspect and mien of a man, which for Classical man is tantamount to the essence and kernel of him. An orator was described as speaking in the prosôpon as a priest or a soldier. The slave was aprosôpos—that is, he had no attitude or figure in the public life—but not asômatos—that is, he did have a soul. The idea that Destiny had assigned the role of king or general to a man was expressed by Romans in the words persona regis, imperatoris.8 The Appollinian cast of life is manifest enough here. What is indicated is not the personality (that is, the unfolding of inward possibilities in active striving), but a permanent and self-contained posture strictly adapted to a so-to-say plastic ideal of being. The significance of Aristotle’s phrase zôon politikon---quite untranslatable and habitually translated with a Western connotation---is that it refers to men who are nothing when single and lonely and only count for anything when in a plurality, in agora or forum, where each reflects his neighbor and thus, acquires a genuine reality. It is all implicit in the phrase sômata poleôs, used for the burghers of the city.
8 prosôpon meant in the older Greek “visage,” and later, in Athens, “mask.” As late as Aristotle the word is not yet in use for “person.” Persona, originally also a theatre-mask, came to have a juristic application, and in Roman Imperial times the pregnant Roman sense of this word affected the Greek prosôpon also.
 The correct translation is in this case, in my opinion, “suspended” because the act of impalement takes place upon the ground or any other flat surface from which the victim is then suspended. Indeed, “suspended” appears in Gunnar Samuelsson, Crucifixionin Antiquity, pp 42-43; whereas “crucified” appears in Martin Hengel, Crucifixion, p. 22, in John Granger Cook, Crucifixion in the Mediterranean World, p. 219, and in the 1920 A.D. Godley translation of Herodotus, The Histories, among others. “Impaled,” on the other hand is mentioned in a translation of The Histories (an introduction and notes by John M. Marincola), p. 224, and in Wikipedia, and also appears in M S M Saifullah, Elias Karim & Abdullah David, Crucifixion or `Crucifiction’ in Ancient Egypt? http://www.islamic-awareness.org/Quran/Contrad/External/Crucify.html, updated 23rd January 2009, accessed 17th September 2010, printout pages 6-7 of 18 (color-format of Latin and brackets mine):
Note how the English translation uses the word “crucified” which is the translation of the Greek anestaurôse from the verb anastaruroô meaning “to impale”. Also notice that the victim Polycrates had already been killed before being crucified. … …
There appears to be no word for “crucifixion” as such in [classical] Greek. The Greek text of Herodotus speaks of “impalement” which is sometimes translated as crucifixion. Herodotus uses the verbs anastaruroô and anaskolopizô both of which mean “to impale”. Generally, he uses the derivatives of the verb anaskolopizô for living persons and anastaruroô for corpses. However, after Herodotus the verbs used to describe the execution in Persia became synonymous with “crucify”, in modern literature. As mentioned earlier, the Greek word for “cross” stauros, which actually denotes an upright stake or pole. The word crux (cross) is Latin and is also the core of several English words including “crucifixion”. In many cases, especially during the Roman period, the execution stake became a vertical pole with a horizontal crossbar placed at some point, and although the period of time this happened is uncertain, what is known is that this simple impalement later became to be known as crucifixion. Whether the victim was tied, nailed or impaled to the stake, the same Greek words were still used to describe the procedure.