Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. An ellipsoid whose three axes represent the refractive indices of an anisotropic crystal for light following different directions with respect to the crystal axes
from the GNU version of the Collaborative International Dictionary of English
 n. A certain conic section supposed to be drawn in the tangent plane to any surface, and used to determine the accidents of curvature of the surface at the point of contact. The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it. It is an ellipse when the curvature is synclastic, and an hyperbola when the curvature is anticlastic.
from The Century Dictionary and Cyclopedia
 n. In geometry, the curve of intersection of any surface with a plane indefinitely near and parallel to the tangentplane at any point.
 n. In the theory of equations, a curve which exhibits the joint effect of the two middle criteria of Newton's rule, in the case of an equation of the fifth degree having all its roots imaginary.
 n. In crystallography, a surface, in general (for a biaxial crystal) an ellipsoid having axes proportional to the principal refractive indexes, whose geometrical characters serve to exhibit the optical relations of the crystal: for a uniaxial crystal the surface becomes a spheroid and for an isotropic crystal a sphere.
Etymologies
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Examples

Quality of a surface such that  by specular reflection or an acute reflection indicatrix  it shows bright reflected lights or the reflected pictures of bright things.

In 1813 he published a pamphlet, "Développement de géométrie pour faire suite à la géométrie pratique de Monge" (Paris, 1813, containing many new and brilliant theories, the most important of which were one relating to the indicatrix of curved surfaces and another on orthogonal surfaces.
The Catholic Encyclopedia, Volume 5: DioceseFathers of Mercy
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