Kato's Crux is a three ball
pattern established by
Idiosensory. The trick simultaneously combines high vertical throws with
rapid catches, creating a structure sort of similar to that of the Sandbox Shuffle.
Kato's Crux has no obvious peers, therefore it is an orphan pattern with no
clear prerequisites beyond basic familiarity with three ball juggling.
To begin learning Kato's Crux, start with one ball in each hand. Cross your non-dominant hand over your dominant hand and then rotate your non-dominant hand so that your palm is facing downward. Then make a fairly high throw from your dominant hand along the center of your body while basically dropping the ball in your non-dominant hand (you should still give the ball a bit of upward movement). In the same motion you are going to uncross and then recross your arms such that your dominant hand is on top, catching the "dropped" ball with your dominant hand as it recrosses. The high ball will then be caught under-the-arm by your non-dominant hand.
As shown, practice this on both sides. To add in the third ball, start with two balls in your dominant hand and one ball in your non-dominant hand. Cross your arms so that they are in the same starting configuration as step one, and then make a fairly high under-the-arm vertical throw from your dominant hand along the non-dominant side of your body. As this ball reaches its peak and begins to descend, you are going to perform the same throws and catches made in step one, except as you uncross your arms you are going to snatch the first ball you threw out of the air before recrossing your arms.
As shown, practice this on both sides. You have essentially completed one full cycle of Kato's Crux. To connect two cycles together, just make a fairly high under-the-arm throw from your non-dominant hand such that it mirrors the very first throw you made (with your dominant hand) before catching the center ball. This will set you up to do another cycle on the the opposite side of your body. Kato's Crux is not a particularly difficult trick to perform, though it will take time to become comfortable with the various throw heights.