20. _The Centraxonia or Grammotypic Ground-Forms._--The second principal group of organic ground-forms, here called grammotypic or centraxonia, is characterised by the fact that a straight line (gramma) or a single principal axis (protaxon) forms the natural centre of the body. This important and extensive group is divided into two subgroups, those with one axis (Monaxonia) and those with crossed axes (Stauraxonia); in the latter different secondary transverse or cross-axes may be distinguished, but not in the former. In the Monaxonia, therefore, every transverse section of the body perpendicular to the principal axis is a circle, in the Stauraxonia, on the contrary, a polygon. The Monaxonia are further subdivided into two groups, in one of which the two poles of the principal axis {xi}are equal and similar (Isopolar), in the other of which they are different (Allopolar); in the former the two halves of the body, which are separated by the equatorial plane (or the largest transverse plane, perpendicular to the principal axis), are equal, in the latter unequal. Among the isopolar uniaxial ground-forms (Monaxonia isopola) may be mentioned the ellipsoidal, spheroidal, lenticular, &c.; to the allopolar uniaxial forms (Monaxonia allopola) belong the conical, hemispherical, ovoid, &c. In the same way the pyramidal ground-forms with crossed axes are divisible into two groups, according as the two poles of the principal axis are equal or not. The ground-form of the former is the double pyramid, that of the latter the single pyramid. Both the double and the single pyramids may again be subdivided, each into two important lesser groups, the regular and the amphithect. In the first division the equatorial plane of the double and the basal plane of the single pyramid is a regular polygon (square, &c.), whilst in the other division it is an elongated or amphithect polygon (rhombus, &c.); the crossed axes are equal in the former, unequal in the latter. (See Gener. Morphol., Bd. i. pp. 416-494.)