98 



MINERALOGY 



rically between the lateral axes. When these six faces are extended, 

 the plus right tetartohedron will be formed, but it is easily seen that 

 the superposition of the two hemihedrons may be so arranged that 

 in place of 2 being selected, 1 and the corresponding faces could 

 have been taken, forming the plus left rhombohedron or 13 could 

 have been selected, the minus right ; or 14, the minus left, thus 

 yielding four possible forms, the plus and minus right, congruent 

 forms, and the plus and minus left, also congruent forms. The 

 rights are not congruent with the lefts. 



Forms 

 I. Rhombohedrons of the third order, 



r/l 



na: 



a : a : me 



n i 



; +r(hkil), + l(ikhl), - r(khil), - l(ihkl). 



When the faces represented by the poles of Fig. 182 are extended, 

 they will inclose space and yield a rhombohedron of the third order, 



Fig. 183, which does not differ in 

 shape from the rhombohedron of 

 the first order; the lateral axes, 

 however, do not end in the central 

 point of the edges, but terminate 

 asymmetrically in the faces on the 

 line drawn between the central 

 points of the zigzag edges. As is 

 shown above, there are four rhom- 

 bohedrons of the third order. Fig. 

 183 is a plus right and Fig. 184 is a plus left rhombohedron of the 

 third order. 



FIG. 184. The Plus Left Rhom- 

 bohedron of the Third Order, 

 (ikfil). 



II. Rhombohedron of the second order 

 (hh2hl), (ahhhl). 



If the poles in Fig. 182 are moved 

 into the diametral planes, it will be 

 the same as revolving the rhombohe- 

 dron of the third order until the lateral 

 terminate in the median point 



TTIC 



of the line drawn between the centers 

 of the zigzag edges. In this position 

 the right form will coincide with the ,-, 



FIG. 185. Rhombohedron 



left, and only plus and minus forms the Second Order, (hh2hi). 



