60 TERMINOLOGY. . 74?. 



or trigrammic Tetragonal-icositetrahedrons, possess three dif- 

 ferent kinds of edges. 



. 74. DIGRAMMIC TETRAGONAL-ICOSITETRAHE- 

 DRONS. 



The digrammic Tetragonal-icositetrahedrons, 

 Fig. 34., are contained under tetragonal faces, 

 which can be divided by one of their diagonals, 

 in two isosceles triangles. 



1. These icositetrahedrons possess three different kinds 

 of solid angles, one of which is formed by three, the others 

 by four faces : all of them are equiangular. The first are 

 monogrammic, eight in number, and correspond to the solid 

 angles of the hexahedron. Of the second, six are mono- 

 grammic, and correspond to the solid angles of the octahe- 

 dron ; the other twelve are digrammic, and correspond to 

 the centres of the faces of the dodecahedron, (. 63.). 



2. These forms possess two kinds of edges, the one 

 terminating in the solid angles of three faces, the other in 

 those which are produced by four equal edges. 



3. The sections and axes are the same as in the hexahe- 

 dron, the octahedron, &c. The rhombohedral axes pass 

 through the solid angles of three faces, the pyramidal axes 

 through the monogrammic, and the prismatic axes through 

 the digrammic solid angles consisting of four faces. 



4. There are two varieties known in nature, of the follow- 

 ing dimensions : 



a. b. c. A. B. 



1. 78 27' 46". 82 15' 3". 117 2 / 8 // . 131 48'36". 14626'33". 



2. 8415'39". 8l25'37". 11253'7". 14454'11". 129 31' 16". 



5. Examples of the first variety of these forms we have 

 in hexahedral Kouphone-spar and dodecahedral Garnet; 

 of the second, in octahedral Fluor-haloide and dodecahedral 

 Corundum ; of both, in hexahedral Iron-pyrites. 



