Three **cuboid conjectures** are three mathematical propositions claiming irreducibility of three univariate polynomials with integer coefficients depending on several integer parameters. They are neither proved nor disproved.

**Cuboid conjecture 1.** *For any two positive coprime integer numbers*
a
≠
u
the eighth degree polynomial

*is irreducible over the ring of integers
Z
*.

**Cuboid conjecture 2.** *For any two positive coprime integer numbers*
p
≠
q
the tenth-degree polynomial

*is irreducible over the ring of integers
Z
*.

**Cuboid conjecture 3.** *For any three positive coprime integer numbers
a
,
b
,
u
such that none of the conditions*

*is fulfilled the twelfth degree polynomial*

*is irreducible over the ring of integers
Z
*.

The conjectures 1, 2, and 3 are related to the perfect cuboid problem. Though they are not equivalent to the perfect cuboid problem, if all of these three conjectures are valid, then no perfect cuboids exist.