Geom. [irreg. f. SYMMETRY + -OID.] Cayley’s name for a certain surface of the fourth order: see quot.

1

1870.  Cayley, Math. Papers, VII. 134. The surface which I call a symmetroid; viz., the surface represented by an equation Δ = 0, where Δ is a symmetrical determinant of the 4th order the several terms whereof are linear functions of the coordinates (x, y, z, w).

2