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Nobody has discovered any perfect cuboid and there is no formula to deliverall possible Euler bricks. During investigations of famous open problemsrelated to the perfect cuboid and Euler brick; I have found some new importantconjectures on Pythagorean triples and biquadratic Diophantine equation [4]which are reduced & quivalence form for perfect cuboid and Euler brickproblems. The details of the conjectures have been provided in Sections 2-3. Ifany perfect cuboid exists it will be only among the solutions of sixconjectures and all the Euler bricks are only among the solutions of next threeconjectures [4]. For example, if any odd $n\in \mathbb{N}$ satisfy$n=e^2-f^2=g^2-h^2=k^2-l^2$ and $e^2f^2=g^2h^2+k^2l^2$; then we can discover aperfect cuboid of type 1 as $\{e^2-f^2,2gh,2kl,g^2+h^2,k^2+l^2,2ef,e^2+f^2\}$having $(e^2-f^2,2gh,2kl)$ having $(e^2-f^2,2gh,2kl)$ as its edges;$(g^2+h^2,k^2+l^2,2ef)$ as its face diagonals and $e^2+f^2$ as its bodydiagonal where $e,f,g,h,k,l~(>1)\in \mathbb{N}$.

Multiple New Important Conjectures on Equivalence to Perfect Cuboid and Euler Brick