. 07. OF SIMPLE FORMS IN PARTICULAR. 55 



the examination of these yields the best means to distill- 

 guish the different varieties of the hexahedral Pentagonal- 

 dodecahedrons. The other edges meet in the monogram- 

 mic solid angles. 



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

 prismatic axes pass through the centres of the characteris- 

 tic edges. 



4. There are three varieties of this form, whose dimen- 

 sions are the following : 



a. b. c. 



1 . 102 35' 40". 108 24' 30". 110 IT 40". 



2. 121 35' 18". 106 36' 2". 102 36' 19". 



3. 141 16' 50". 103 20' 33". 96 1' 2". 



A. B. 



1. 112 37' 12". 11729 / 11 // . 



2. 126 52' 12". 113 34' 41". 



3. 143 7' 48". 107 27' 27". 



5. The first and second variety are found in hexahedral 

 Iron-pyrites, the angles of the third depend upon the third 

 variety of the icositetrahedrons, . 71- 130. 



. 67. TETRAHEDRAL PENTAGONAL-DODECAHE- 

 DRONS. 



The faces of the tetrahedral Pentagonal-dodeca- 

 hedrons, Figs. 21. 22. 23. 21, have no equal angles ; 

 but they possess two pairs of equal sides. 



1. The tetrahedral Pentagonal-dodecahedrons have three 

 kinds of solid angles, all of which are formed by three faces. 

 The first are equiangular, monogrammic, four in number, 

 and they correspond to the solid angles of the tetrahedron ; 

 the second, of the same description, but more obtuse, cor. 

 respond to the centres of the faces of the same form. The 

 third are not equiangular ; they are trigrammic, twelve in 

 number, and pairs of them are situated between the more 

 acute equiangular solid angles. 



