54 TERMINOLOGY. . 65. 66. 



4. The sections and axes are as in the tetrahedron. The 

 prismatic axes pass through the solid angles of four faces. 



5. There is only one variety known of this form, whose 

 dimensions are the following : 



a. b. e. A. B. 



90. 118 4' 10". 75 67' 55". 90. 152 44' 2". 



6. It has been observed in dodecahedral Garnet-blende. 



. 65. PENTAGONAL-DODECAHEDRONS. 



The Pentagonal-dodecahedrons are contained un- 

 der equal and similar pentagons. 



1. There are two kinds of Pentagonal-dodecahedrons. 



2. In the one, every face has the opposite one parallel to 

 it, a property which is not to be met with in the other. 



3. The first have the general aspect of the hexahedron, 

 and are therefore termed Iwxahedral ; the other that of the 

 tetrahedron ; and accordingly they bear the denomination 

 of tetraJiedral Pentagonal-dodecahedrons. 



.66. HEXAHEDRAL PENTAGONAL-DODECAHEDRONS. 



The faces of the hexahedral Pentagonal-dodeca- 

 hedrons, Figs. 19. 20., have two pairs of equal angles, 

 and four equal sides. The single angle is opposite 

 to the single side. 



1. All the solid angles of these Pentagonal-dodecahe- 

 drons, are bounded by three faces ; eight of them are equi- 

 angular and monogrammic, and correspond to the solid 

 angles of the hexahedron. The other twelve are formed 

 by two equal angles, and the single angle ; they are di- 

 grammic, and pairs of them may be conceived to be situated 

 upon the faces of the hexahedron, in the direction of 

 planes, which pass through two pyramidal axes of that form. 



2. Of the two kinds of edges, those opposite to the single 

 angle are the Characteristic Edges of this form ; because 



