Hagendorfite is an iron with the chemical formula of (Na,Ca)MnFe 2(PO 4) 3 and is named after where the mineral was discovered, Hagendorf-Süd, Bavaria
Hagendorfite is in the monoclinic crystal class; the mineral's internal symmetry consists of three axes with unequal length. Furthermore, the angles between two of the axes is 90° while the other angle is less than 90°. Monoclinic minerals contain a twofold rotation axis where they can be rotated 360° and have the crystal face repeat every 180°. They also have the characteristic mirror plane, which can produce a perfect mirror image when divided in two.
Hagendorfite belongs to the monoclinic crystal class, so it is assigned to the biaxial optical class. Hagendorfite's optic sign, which is negative, is proven by examining its interference figure. Biaxial minerals, including Hagendorfite, have three indices of refraction which may or may not correspond with the mineral's unequally lengthened axes. A refractive index will provide the ratio of the speed of light in a vacuum with the speed of light in the mineral. A single refractive index is given when two rays of light vibrate in the mineral's circular section and move along the optic axes.