. 131. OF THE CONNEXION OF FORMS. 139 



ternating faces contiguous to the principal points disap- 

 pear, and at the same time those which are parallel to the 

 former at the subordinate points; every one of the re- 

 maining enlarged faces is intersected by five others, and 

 thus assumes a pentagonal figure. The number of faces ig 

 evidently twelve ; the form produced will therefore be a 

 pentagonal-dodecahedron, which is a hexahedral one because 

 the second mode of resolution does not change the general 

 aspect of the form. The latter property also might be 

 derived from the equality and similarity of the eight solid 

 angles of three faces, which correspond to those of the 

 hexahedral trigonal-icositetrahedron, which are formed by 

 six faces (. 66. !.) 



The crystallographic signs of the hexahedral pentagonal- 

 dodecahedrons, one of them being in the normal, the other 



in the inverse position, Figs. 19. 20., are (a) and 



(a'), where n denotes the variety which is to be 

 expressed. 



. 131. THE DIGBAMMIC TETRAGONAL-DODECAHE- 

 DRON. 



The half of the octahedral trigonal-icositetrahe- 

 dron is the digrammic Tetragonal-dodecahedron 

 (. 64.). 



The resolution is effected after the first method. 



Each of the enlarged faces is intersecte'd by four others, 

 of which two belong to the same, and two to other princi- 

 pal points. Th us they become four-sided, and their number 

 is twelve. Hence the form is a tetragonal-dodecahedron ; 

 and since it assumes the general aspect of a tetrahedron, 

 the first mode of resolution having been applied, it will be 

 that described in . 64. 1., or the digrammic tetragonal- 

 dodecahedron. 



The crystallographic signs of these forms in the normal 



