What is the correct order of directions for shaking the lulav?

Question

I remember last year seeing two different orders of directions for shaking the lulav. In one case people did left, right, front, back, up, down, while in the other they did front, right, back, left, up, down (so "going around the circle", clockwise from front). Is there a "correct" order, or is this just a matter of personal minhag (and people tend to follow the leader)? If there's variation, which communities do it which way?

Answer 1

Qitzur Shulhhan 'Arukh, Yalqut Yosef (Orahh Hayim 651:45) states (my translation):

אחר שבירך, ינענע הלולב ומיניו שלש פעמים לכל צד. ואף על פי שהוא עתיד לנענע בשעת ההלל, יעשה הנענועים גם עתה אחר הברכה, ללא אומר ודברים. ודעת מרן שבנענוע צריך להקיף דרך ימין, שהוא לצד מזרח דרום מערב צפון. אבל המנהג פעיה''ק ירושלים ת''ו כמו שכתב רבינו האר''י, להקיף דרום צפון מזרח מעלה מטה ומערב. ואין לשנות. וכל עדה תחזיק במנהגה, אבל על כולם לעשות סדר הנענועים כסברא אחת, או כסברת מרן השלחן ערוך, או כפי מנהגינו כדעת האר''י ז''ל, ולא יהיו חלוקים במנהגם [...].

After one recites the blessing, one should wave the Lulav and its species three times in each direction. And, even though one will perform the wavings during Hallel, one should perform the wavings now after reciting the blessing. And, according to Maran (i.e. Shulhhan 'Arukh), one should encircle oneself while performing the wavings by turning to one's right (i.e. by waving Eastward, Southward, Westward and finally Northward).

Nevertheless, the minhag in the Holy City of Jerusalem (she should be and stay built) follows the writings of Rabbeinu HaAR"I, which is to encircle oneself by waving Southward, Northward, Eastward, Upward, Downward and finally Westward. And this custom should not be altered.

And each community should hold by its own custom; but, should ensure that all perform the wavings according to the community's custom, or according to the custom of Maran HaShulhhan Arukh, or according to our custom which adheres to the opinion of HaAR"I Z"L. And, they should ensure not to be divided in their customs.

As such, it appears the manner of waving Arba'at HaMinim is a matter of minhag rather than strict Halakhah.

Answer 2

The Shulchan Aruch (OC 651:10) indicates that the order is forward, right, backward, left (followed by up then down, as indicated by the Mishna B'rura). This is echoed by other acharonim, and, according to the Magen Avraham, even a lefty should follow this order. The Mishna B'rura writes that "this order of the na'anu'im accords with the practice in our lands" (ibid. 651:47).