A quartic surface which is the locus of zeros of the determinant of a symmetric 
matrix of linear forms. A general
symmetroid has 10 ordinary double points
(Jessop 1916, Hunt 1996).
Symmetroid
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References
Hunt, B. "Algebraic Surfaces." http://www.mathematik.uni-kl.de/~hunt/drawings.html.Hunt, B. "Symmetroids and Weddle Surfaces." §B.5.3 in The Geometry of Some Special Arithmetic Quotients. New York: Springer-Verlag, pp. 315-319, 1996.Jessop, C. Quartic Surfaces with Singular Points. Cambridge, England: Cambridge University Press, p. 166, 1916.Referenced on Wolfram|Alpha
SymmetroidCite this as:
Weisstein, Eric W. "Symmetroid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Symmetroid.html