TEHMIXOLOGY. . 134. 



If we apply the third method, the result will be a pen- 

 tagonal-icositetrahedron. Here all the alternating faces 

 of the original form are enlarged, while the rest disappear, 

 so that each face is intersected by five others, of which two 

 belong to the same principal point, the rest to the adjoin- 

 ing subordinate points, and the faces assume therefore a 

 pentagonal figure. Of the pyramidal solid angle of the te- 

 tracontaoctahedron likewise the alternating faces are en- 

 larged ; this solid angle therefore remains a pyramidal one, 

 and the axis which passes through it, a pyramidal axis. 

 These properties will suffice for determining the form to be 

 a pentagonal icositetrahedron. 



The crystallographic signs of the pentagonal-icositetra- 

 hedrons, in reference to their being as it were twisted to 



the right or to the left, Figs. 29. 30., are r IL^ and 1 ~~. 



2 2 



It would be superfluous to add here the number iii for in- 

 dicating the mode of resolution, except in comparing these 

 forms with other halves of the tetracontaoctahedron. 



. 134-. THE TETRAHEDRAL PENTAGONAL-DODE- 

 CAHEDRONS. 



The three icositetrahedrons of the preceding pa- 

 ragraph, which are halves of the tetracontaoctahe- 

 dron, allow of a farther resolution, and then yield 

 the fourths of that form, The fourths of the te- 

 tracontaoctahedron, are the tetrahedral Pentagonal- 

 dodecahedrons (. 67.). 



The resolution of the tetrahedral trigonal-icositetrahe- 

 dron, is effected by enlarging its alternating faces, till they 

 limit the space by themselves. Each of the enlarged faces 

 is intersected by five others ; and the resultant fourth is 

 therefore a pentagonal-dodecahedron, whose general aspect 

 is that of the tetrahedron, on account of the application of 

 the first process. The fourth itself is the tetrahedral 

 pentagonal-dodecahedron. 



