# 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.**Fig. 5.**

*A visualization of the 3D CPF.*

*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)

$R'_B=\frac{R_AR_B}{R'_A}=\frac{R_AR_B}{R_A+r_A}$

.Last modified 1yr ago