The flattened sphere, or facetted sphere (_platnosphæra_), is known as an endospherical polyhedron; that is to say, a many-surfaced body, all the corners of which fall in the surface of a sphere. The axes or the diameters, which are drawn through the angles and the centre, are all unequal, and larger than all other axes (drawn through the facets). These facetted spheres are frequently found in the globular silicious skeletons of many of the radiolaria; the globular central capsule of many spheroidea is enclosed in a concentric gelatine envelope, on the round surface of which we find a net-work of fine silicious threads. The meshes of this net are sometimes regular (generally triangular or hexagonal), sometimes irregular; frequently starlike silicious needles rise from the knots of the net-work (A-f, 1, 51, 91). The pollen bodies in the flower-dust of many flowering plants also often assume the form of facetted spheres. II. CENTRAXONIA TYPES.--The natural middle of the body is a straight line, the principal axis. This large group of fundamental forms consists of two classes, according as each axis is the sole fixed ideal axis of the body, or other fixed transverse axes may also be distinguished, cutting the first at right angles. We call the former uniaxial (_monaxonia_), and the latter transverse-axial (_stauraxonia_). The horizontal section (vertically to the chief axis) is round in the uniaxials and polygonal in the transverse-axial. In the monaxonia the form is determined by a single fixed axis, the principle axis; the two poles may be either equal (_isopola_) or unequal (_allopola_). To the isopola belong the familiar simple forms which are distinguished in geometry as spheroids, biconvex, ellipsoids, double cones, cylinders, etc. A horizontal section, passing through the middle of the vertical chief axis, divides the body into two corresponding halves. On the other hand, many of the parts are unequal in size and shape in the _allopola_. The upper pole or vertex differs from the basal pole or ground surface; as we find in the oval form, the planoconvex lens, the hemisphere, the cone, etc. Both sub-classes of the monaxonia, the allopola (conoidal) and the isopola (spheroidal), are found realized frequently in organic forms, both in the tissue-cells of the histona and the independently living protists (A-f, 4, 84). In the stauraxonia the vertical imaginary principal axis is cut by two or more horizontal cross-axes or radial-axes. This is the case in the forms which were formerly generally classed as regular or radial. Here also, as with the monaxonia, we may distinguish two sub-classes, isopola and allopola, according as the poles of the principal axis are equal or unequal.