Who first used the word "Simplex"?

According to Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics, the first known occurrence is in Schoute’s Mehrdimensionale Geometrie of 1902.

The earliest references found by Google date back to 1909. W.H. Bussey mentions it in an article from that year, On the tactical problem of Steiner published in the Bulletin of the AMS. Precisely, what he defines to be a simplex is the boundary of what is called a simplex today:

The $l+1$ points of such a set, if taken $l$ at a time, determine a number of $l-1$-spaces whose points constitute a set that may conveniently be called a simplex$^*$ of order $l$. The $l + 1$ points are called vertices.

$^*$*The word is used in geometry of n-dimensions to denote the configuration analogous to the triangle in the plane or the tetrahedron in 3-space.

http://www.ams.org/journals/bull/1909-16-01/S0002-9904-1909-01845-2/S0002-9904-1909-01845-2.pdf