The bisphenoids (the hemihedral forms of the tetragonal and rhombic bipyramids)., and the trigonal pyramid of the hexagonal system, are examples of non-regular tetrahedra (see Crystallography).
(The stereo-chemistry of carbon compounds has led to the spatial representation of a carbon atom as being situated at the centre of a tetrahedron, the four valencies being directed towards the apices; see above, and Isomerism.) A form based on Kekule's formula consists in taking three pairs of tetrahedra, each pair having a side in common, and joining them up along the sides of a regular hexagon by means of their apices.
Arrangements connected with Claus' formula are obtained by placing six tetrahedra on the six triangles formed by the diagonals of a plane hexagon.
The form in which the tetrahedra are all on one side, afterwards discussed by J.
Loschmidt (Monats., 1890, II, p. 28), would not give stereo-isomers; and the arrangement of placing the tetrahedra on alternate sides, a form afterwards developed by W.
Two parallel triangular faces are removed from a cardboard model of a regular octahedron, and on the remaining six faces tetrahedra are then placed; the hydrogen atoms are at the free angles.
Then the prismoid is divided into a pyramid with vertex P and base ABCD ..., and a series of tetrahedra, such as PABa or PAab.
Respectively, and a series of tetrahedra having Q as one vertex.
5 shows how the octahedron with furrowed edge may be constructed from two interpenetrating tetrahedra (shown in dotted lines).
R shows a combination of two tetrahedra, in which the four faces of one tetrahedron are larger than the four faces of the other; further, the two sets of faces differ in surface FIG.
Beautiful isolated tetrahedra of transparent yellow blende are found in the snow-white crystalline dolomite of the Binnenthal in the Valais, Switzerland.