This set of documents (primarily about the iconography of the Large Glass – Fig.7) has only a few references to geometry. However dimensionality was present in Duchamp's life and it was a subject explored in this document:

The negative apparition (determined conventionally by the linear perspective but always in an environment of n-1 dimensions. for an object of n dimensions)
Duchamp, Green Box

These direct references to “n dimensions” are rare but the 4th dimension is a crucial idea through out the Green Box. Duchamp wanted some of the elements described in this box to relate effectively to the fourth dimension (Fig. 8):

[…] any three dimensional object, which we see dispassionately, is a projection of any three-dimensional object, something we are not familiar with. It was a bit of sophism, but still it was possible. “The Bride” in the “Large Glass” was based on this, as if it were the projection of a four-dimensional object.

Duchamp, as quoted in Cabanne, 1971, page 40