In abstract algebra, the trigintaduonions, also known as the 32-ions, 32-nions, 2⁵-nions form a 32-dimensional noncommutative and nonassociative algebra over the real numbers.

The word trigintaduonion is derived from Latin triginta 'thirty' + duo 'two' + the suffix -nion, which is used for hypercomplex number systems. Other names include 32-ion, 32-nion, 2⁵-ion, and 2⁵-nion.

Every trigintaduonion is a linear combination of the unit trigintaduonions ${\displaystyle e_{0}}$, ${\displaystyle e_{1}}$, ${\displaystyle e_{2}}$, ${\displaystyle e_{3}}$, ..., ${\displaystyle e_{31}}$, which form a basis of the vector space of trigintaduonions. Every trigintaduonion can be represented in the form

with real coefficients x_i.

The trigintaduonions can be obtained by applying the Cayley–Dickson construction to the sedenions. Applying the Cayley–Dickson construction to the trigintaduonions yields a 64-dimensional algebra called the 64-ions, 64-nions, sexagintaquatronions, or sexagintaquattuornions.

As a result, the trigintaduonions can also be defined as the following.

An algebra of dimension 4 over the octonions ${\displaystyle \mathbb {O} }$:

An algebra of dimension 8 over quaternions ${\displaystyle \mathbb {H} }$: