## Crossed-V-Variations

#### October 2020

Crossed-V-Variations are, as the Scrambled-V-Variations, a group of manipulation patterns with four persons: 3 jugglers $$\{A, B, C\}$$ and a manipulator $$M$$. In distinction to the Scrambled-V-Variations, a different feed transition is used, which results in a change of the handedness after every transition.

The feed transition. Instead of using the "standard feed transition" (also called left pentagon in [1]). Crossed-V-Variations are based on the feed transition, described here as right (line). It goes as follows:

##### Fig 1. For better readability, we change the orientation so that the pattern is moving to the right. We further change the labeling according to the current standards.

At the first transition, Juggler $$B$$ is changing to the position to the right of juggler $$A$$ and becomes $$C'$$. During the walking time of $$B$$, a pass between the two other passers is taking place. This pass is already the pass at beat one of the iteration, where $$C \rightarrow A'$$ and $$A \rightarrow B'$$ respectively. Note that in this transition the handedness changes from right to left and vise versa on every transition. This means, starting with right-handed passes, all passes are thrown with the left hand after the transition (see Fig.1). We mark this by $$A'$$, $$B'$$ and $$C'$$. Notice that due to this change, $$C$$ will have a 5-count and $$A$$ a 3-count.

##### Table 1. Beats and actions of the jugglers.
 Beats 1 2 3 4 5 6 7 $$A$$ $$P_B$$ $$S$$ $$P_C$$ $$S$$ $$P_B$$ $$S$$ $$S$$ $$\rightarrow B'$$ $$B$$ $$P_A$$ $$S$$ $$S$$ $$S$$ $$P_A$$ $$S^*$$ $$S^*$$ $$\rightarrow C'$$ $$C$$ $$S$$ $$S$$ $$P_A$$ $$S$$ $$S$$ $$S$$ $$S$$ $$\rightarrow A'$$
##### $$^*$$Do not throw: We find it quite hard to do the transition while juggling. It is much easier to walk without juggling, since one is going through the pattern.

With Manipulation. The manipulation sequence follows the one of the Scrambled-V-Variations. However due to the change of the handedness, one will have a certain role only with on the right or on the left handed side, never on both.

##### Table 2. The positions of jugglers and their roles including left and right handedness.
 R L R L $$P_1$$ $$P_2$$ $$P_3$$ $$P_4$$ $$J_1$$ $$A$$ $$\rightarrow$$ $$B'$$ $$\rightarrow$$ $$C$$ $$\rightarrow$$ $$M'$$ $$J_2$$ $$B$$ $$\rightarrow$$ $$C'$$ $$\rightarrow$$ $$M$$ $$\rightarrow$$ $$A'$$ $$J_3$$ $$C$$ $$\rightarrow$$ $$M'$$ $$\rightarrow$$ $$A$$ $$\rightarrow$$ $$B'$$ $$J_4$$ $$M$$ $$\rightarrow$$ $$A'$$ $$\rightarrow$$ $$B$$ $$\rightarrow$$ $$C'$$
As shown above in the table, $$J_1 \equiv J_3$$ and $$J_2 \equiv J_4$$ according to their permutation.

We found it much easier not to juggle during the walking, since it can get quite crowded inside the pattern. It is recommended to count loud, since it happens that during the transition that just one juggler is juggling.

Fun Fact: The underlying feed transition encompasses 5 transitions (6 to get to the starting allocation).
However, introducing a manipulator shortens the number of transitions to 3 (4 to get tp the starting allocation respectively).

$$A \rightarrow B' \rightarrow C \rightarrow A' \rightarrow B \rightarrow C' \rightarrow A$$