Is This 1624 Polish Coin I.d.'d Correctly?

I have one of these that I thought was 1624 for months. Turned out to be 1626 - I was looking for the date in the wrong place (this one is definitely 1624 though!)

Other than that, as far as I can tell it indeed is a dreipolker/poltorak (no idea if naming it "3 polker" makes sense though).

Fun fact about this type: that's SIGIS 3 on the top right here, which stands for Sigismund III - which makes this the only coin type I'm aware of (there are probably many I'm not aware of) where the regnal number is expressed as an Arabic numeral (basically everyone else used Roman, as in III).

It was minted in Bydgoszcz and the king's full name in English is Sigismund III Vasa.

The Polish-Lithuanian Commonwealth was fairly unique amongst European governments of the late mediaeval and early modern period, in being an electoral monarchy in practice rather than just in theory, as the kingdoms of Germany and Bohemia were. That is, whenever the old king died, the parliament of noblemen convened to decide who would be the next king. It was also unusual in the sheer size of the electorate, with some 100,000 noblemen theoretically allowed to vote - compared with just seven Electors in Germany, for example.

Unfortunately, it did not take the other European nations long to realise that this system could be rorted for their own personal gain. At Election time, Poland's neighbours would send "delegations", ostensibly to lobby the noblemen but in reality to threaten violence and invasion if their candidate did not win.

And you thought political lobbying in your country was out of hand.

Sigismund III Vasa was the son of King John III of Sweden but, since he was a Catholic and Sweden was officially Protestant, he could not inherit the throne. So he returned to his mother's ancestral homeland to try his luck there. His main rival at the 1587 Election was Maximilian III, fourth son of the Austrian emperor, Archduke of Further Austria and Grand Master of the Teutonic Order (which owned several cities on the Baltic coast). Austrian troops invaded in retaliation when Maximilian lost the election, but after a year of intermittent conflict the Austrians were soundly defeated by Commonwealth forces. He eventually became king of Sweden too in 1592, but concern at his militant anti-Protestantism saw popular revolt there and he was deposed from Sweden again in 1599.

It was Sigismund III who was also responsible for initially converting the territory of what is now north-western Ukraine from Eastern Orthodoxy to a form of Roman Catholicism; in that sense, we are seeing the legacy of his rule even today in the current Ukraine Crisis.

It should also be pointed out, if you were not yet aware of it, that the two halves of the Commonwealth - the Kingdom of Poland and the Grand Duchy of Lithuania - had separate governments and separate coinages, much like the situation in the Austro-Hungarian Empire a few centuries later. Your coin is from the Polish half, which is why you will find it listed under "Poland" in the catalogues. Although both halves of the country are mentioned in the king's titles on the obverse (REX P. = King of Poland, M.D.L. = Grand Duke of Lithuania), the Latin inscription on the reverse (MONE NO REG POLO = New Money of the Kingdom of Poland) and the pre-eminence given to the Polish Eagle rather than the Lithuanian Horse-and-Rider on the coat of arms both indicate that this is a Polish coin. Here's a Lithuanian coin from much the same time period.

Date (16)24 is left and right from the cross
Denom is 3 polker or 1/24th thaler (24 under the globe)
Sigismund III VASA (1587-1632), king of poland and sweden : http://en.wikipedia.org/wiki/Sigismund_III_Vasa
3 POLKER (3 Poltorak - 1 Kruzierz) (16)24,
MONE*NO*REG*POLO
MONETA NOVA REGIS POLONIAE
new coin of the kingdom Poland
SIGIS 3 DG REX P M D L
SIGISMUNDO TERTIO DEI GRATIA REX POLONIAE MAGNUS DUX LITHUANIAE
Sigismund the 3th, by the grace of gods, king of Poland, Grand duchy of Lithuania
BYDGOSZCZ (Bromberg) mint
B.24 on http://forum.tpzn.pl/index.php?topic=3129.15
centershield : sheaf of grain of king Wasa : http://upload.wikimedia.org/wikiped...Vasa_CoA.svg
mintmaster : Mikołaj Daniłowicz, ministre of finance (podskarbi koronny)(Arrow and two stars) : http://en.wikipedia.org/wiki/Miko%C...i%C5%82owicz

Awalin, that is what coin collecting makes worthwhile. I must Always know as much as possible about the coin, the ruler, the period...
Here you find a coin of the same period as yours, same ruler, but as king of Sweden (REX S and REG SVE = SVECLAE, Sweden)and Elbing mint (heart with two arrows)
It can be 'Duke of' or 'duchy of'. I found a lot of contradiction in several books.
New Money is indeed a better translation form latin