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NEW YORK STATE MUSEUM 



as the phis and minus pyritohedrons do to the tetrahexahedron. 

 Fig. 50-52 show combinations of forms in this group and rep- 

 resent crystals of pyrite and cobaltite. 



Tetrahedral group 

 The general symmetry of this group is shown in fig. 53. The 

 crystallographic axes are axes of binary symmetry and the crys- 

 tals of this type are symmetric to the six 

 white planes of fig. 28. The cube, dodeca- 

 hedron and tetrahexahedron occur in this 

 group but are readily distinguished from 

 the same forms of the normal type by the 

 degree of symmetry shown in their combi- 



nations with other forms. The axes of trigo- 



Fig. 53 



nal symmetry indicated in fig. 53 constitute 

 a characteristic feature of the group. 



Tetrahedron. The tetrahedron (fig. 54, 55, model 5) is com- 

 posed of four equilateral triangular faces each of which meets 



Fig. 54 Fig. 55 



the axes at equal distances. Two tetrahedrons are possible and 

 are known as plus (fig. 54) and minus (fig. 55), the eight faces 

 composing them corresponding to the eight like faces of the 

 octahedron. 



Trigonal tristetrahedron. The trigonal tristetrahedron (fig. 56, 

 57) is composed of 12 triangular faces each of which meets 

 t wo axes at equal distances and the third at a distance which 

 is relatively less than the intercept on the other two. A plus 

 Trigonal tristetrahedron is shown in fig. 56 and the correspond- 

 ing minus form in fig. 57; these bear a relation to the trapezo- 



