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.
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