A tetrahedroid is a special quartic surface in the family of Kummer surfaces, with four planes forming a tetrahedron and each containing exactly four of its 16 ordinary double points (Elsenhans and Jahnel 2012, pp. 90-91). The cross sections by the faces of this tetrahedron are pairs of conics over the complex numbers meeting at those four ordinary double points.
A symmetric example in homogeneous coordinates 
is
 |
Its 16 ordinary double points are
 |
with the signs chosen independently in each group. Thus each coordinate plane contains four ordinary double points. Setting
gives an affine equation of the form
also used for the Kummer surface.
The illustration uses affine coordinates in the coordinate chart 
to show the real locus
of this symmetric example, with all 16 ordinary
double points marked in red. The quartic surface
is clipped to a finite box.
The tetrahedroids form a two-dimensional subfamily of the three-dimensional family of Kummer quartics (Elsenhans and Jahnel 2012, p. 91).
