# The Triad Pool

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.

![Fig. 5. A visualization of the 3D CPF.](https://lh3.googleusercontent.com/fO5NVw3oYzA1e2V-B99CFkzTPOzquICEsSRoWPhohkaz3M5wSNMz43V-PVOOPo_Pm3IUAyeYy8sUT7ebg_bOuu5QVzhDDiXjrRn2zlSFk5QuG7g8LP2WTKucLiEogl1u8MC_751v)

***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*](/litepaper/sen-as-the-heart-of-the-ecosystem/asymmetric-deposit.md)). 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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