TITLE: Who first used the word "Simplex"?
QUESTION [17 upvotes]: Who first used the word "Simplex" to describe the considered geometric figure?

REPLY [19 votes]: 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.

REPLY [8 votes]: 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