# The Triad Pool

Swap any and every pairs. Never think about how you should divide your portfolio ever again.

Recall that the most well-adopted CPF is two-dimensional where $R_A\times{R_B}=k$. In Sentre, however, the pool can be optionally organized into three tokens. It’s now the pool of triad and the CPF turns to three-dimensional where the third dimension is for $SEN$ as in Fig. 5.

**Definition 3.*** For a pool of *$A$,* *$B$, *and compulsory *$SEN$*, the 3D constant product function is:*

*(33) *$R_A\times{R_B}\times{R_{SEN}}=k$*,*

*where *$k$* is a constant.*

To deposit to the pool, a liquidity provider (LP) theoretically needs to divide their portfolio into three equal portions regarding value. However, LPs never worry about this due to **Simulated Single Exposure** which allows people to deposit even on one side (see *Asymmetric Deposit*). Especially, although the formula has a higher dimension, the formula isn’t much different from the 2D CPF in trading.

When a trader swaps* *$A$** **from* *$B$, for example, the third token, which is $SEN$ in this case, will be ignored. The formula is boiled down to $R_A\times{R_B}=\frac{k}{R_{SEN}}=k'$, where $k'$ is a constant as well.

Assume a trader swaps * *$r_A$** **for $r_B$, the newest state of token $A$ would be $R'_A=R_A+r_A$. Because of the CPF, we have:

(34) $R'_B=\frac{R_AR_B}{R'_A}=\frac{R_AR_B}{R_A+r_A}$.

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