. 75. OF SIMPLE FORMS IN PARTICULAR. Gl 



. 75. TRIGRAMMIC TETRAGONAL-ICOSITETRAHE- 

 DRONS. 



The trigrammic Tetragon al-icosi tetrahedrons, 

 Figs. 27. 28., are contained under tetragonal faces, 

 which cannot be divided in two isosceles triangles by 

 any of their diagonals. 



1. The angles of these forms consist of either three or 

 four faces. The first are monogrammic, equiangular, eight 

 in number, and they are situated like the solid angles of 

 the hexahedron. Of the solid angles of four faces, six are 

 equiangular and digrammic, and they are distributed like 

 the solid angles of the octahedron ; the other twelve are un- 

 equiangular and trigrammic, and they have the situation of 

 the digrammic solid angles in the hexahedral pentagonal- 

 dodecahedron (. 66. 1.). 



2. Of the three different kinds of edges, the first termi- 

 nate in the solid angles consisting of three faces ; the first 

 and second in the digrammic, and the first, second, and 

 third, in the trigrammic solid angles, bounded by four faces. 



3. The mutual inclination NOP of the longest or greatest 

 edges, in the digrammic solid angle, is the Characteristic Angle 

 D of the trigrammic tetragonal-icositetrahedron. 



4. The sections and axes are the same as those of the 

 hexahedral pentagonal-dodecahedrons; the rhombohedral 

 axes pass through the solid angles of three faces, the pris- 

 matic axes through the digrammic solid angles of four faces. 



5. There are three varieties of these forms, whose dimen- 

 sions are as follows : 



a. b. c. d. 



1- 106 59' 7". 79 53' 50". 116 6' 13". 57 0' 50". 



2. 104 38' 25". 84 12' 32". 113 21' 46". 57 47' 17". 



3. 96 13' 37". 83 46' 23". 113 34' 41". 66 25' 19". 



A. B. C. D. 



1. 148 59' 50". 115 22' 37". 141 47' 12". 112 37' 12". 



2. 160 32' 13". 118 59' 9". 131 4' 57". 118 4' 10". 



3. 154 47' 28". 128 14' 48". 131 48' 37". 126 52' 12". 



