What is the earliest attested mention of the fact that a parallelepiped in Euclidean 3-space can be decomposed into six tetrahedra?

Question

• The question is in the title.

• A pictorial representation of what this is about is the following:

_{(created with GeoGebra and GIMP)}

• The orthoschemes named after Ludwig Schläfli are very relevant but more special, and I suspect that the above decomposition has been recognizably described much earlier than the mid 1800s.

• I would also appreciate a view on whether this recognizably occurs in Euclid's elements. To me it seems it doesn't.

• Are there attested extant non-European mentionings of this?