each
face of the inscribed tetrahedron, and twelve interme diate in pairs
over its edges. The angles are six rhombic, joined in pairs by the
principal axes, and four acuter and four obtuser hexagonal angles.—Ex.,
diamond.
The
derivation and signs of these forms are as follows :— The tetrahedron
arises when four alternate faces of the octahedron are enlarged, so as
to obliterate the other four,
and its sign is hence O/2. But, as either four faces may be
thus
enlarged or obliterated, two tetrahedrons can be formed similar in all
respects except in position, and together making up the octahedron.
These are distinguished by the signs + and —, added to the above
symbol, but only the
latter in general expressed thus ——. In all hemihedric
systems
two forms similarly related occur, which may thus be named
complementary forms. The trigonal dodecahedron is derived from the
icositetrahedron, by the expansion
of the alternate trigonal groups of faces. Its sign is —--—,
