THE SYMMETRIES OF CRYSTALS 583 



the trapezahedron, are placed beside their parent forms, and the hexa- 

 tetrahedron (k), the half form of the hexoctahedron, is placed necessar- 

 ily above the latter, from its relation to the tetrahedron. 



In accord with the second law, the four-faced cube gives rise to the 

 pentagonal dodecahedron (I) which is placed above it, and the central 

 figure, the hexoctahedron (g) gives rise to the diploid (n) which is 

 placed naturally just above its associate the pentagonal dodecahedron. 



There remains the single gyroidal form (n) obtained by the third 

 law, which is placed directly beneath the central figure (g) from which 

 it was derived. 



An inspection of the figure will show that the triangle with which 

 we began, the mason's symbol of the trinity, has most naturally de- 

 veloped itself into the form of a cross. Isolated on either side stand the 

 cube and dodecahedron, two unique forms not capable of change or con- 

 version into any other form, like the two thieves beside the cross. But 

 said one of my friends, who is a good crystallographer, as I called her 

 attention to this similitude, one of the thieves was converted. 



This would seem to throw doubt on the record, I replied, and yet 

 there are infinite possibilities present, as one sees, in the formula?, 

 1 : x> :x, 1 : 1 : ». 



One observes next that the five Platonic forms find symmetrical 



place on the figure : two at the top, two at the lower corners and one — 



the icosahedron — by evenly balanced combination of the top and bot- 



12 1 

 torn of the figure. Ill, 



The cross may be a cross of gold or of any other of the noble metals, 

 and an inspection of the figure shows further that it culminates in an 

 upper triangle placed like a crescent above the cross which contains the 

 perfect forms attained by the perfect mineral, the diamond. At the 

 center of this triangle is the tetrahedron (h) which gives the model of 

 the atom of carbon and the hexatetradon (Jc) the most typical form of 

 the diamond itself. 



So again in a new arrangement of the elements in accord with the 

 periodic law, proposed by the writer, 1 carbon is the culmination of the 

 first octave and the very center and omphalos around which all the ele- 

 ments circle in their grand evolution. It has four-fold valence and 

 threefold allotrophism and stands as the center of the seven elements 

 of the first octant. And as the diamond is brought down from the 

 heavens in the meteorites and brought up from the depths of the earth 

 with the deepest rocks, and as it is endowed with the greatest power 

 over light and over all solid bodies, so it presents in its almost spherical 

 hexatetrahedron a mean around which the earth seems many times to 

 have oscillated, as Arldt has shown, 2 now varying slightly toward the 

 tetrahedron; now almost recovering again the spheroidal form. 



1 "Helix Chemica," Am. Chem. Jour., Vol. XLV., p. 160, 1911. 



2 Dr. Theodor Arldt, "Die Entwickelung der Kontinente, " Leipzig, 1907. 



