. 69. 70. 01- ' SIMl'LE FORMS IX PARTICULAR. 57 



1. None of these kosi tetrahedrons are geometrically re- 

 gular. 



. 69. TRIGONALrlCOSITETRAHEDRONS. 



The Trigonal-icositetrahedrons are contained un^ 

 der equal and similar, isosceles or scalene triangles. 



1. This species of icositetrahedrons comprises three 

 kinds, different from each other by their general aspect, 

 and the situation of their faces. 



2. The varieties of the first kind have no parallel faces ; 

 they exhibit the general aspect of the tetrahedron, and are 

 therefore said to be tetrahedral ; the varieties of the second 

 have parallel faces, and the general aspect of the hexahe- 

 dron ; these are termed hcxahcdral ; the varieties of the 

 third possess also parallel faces, but the general aspect of 

 the octahedron, and these are termed octahedral Trigoual- 

 icositetrahedrons. 



. 70. TETRAHEDRAL TRIGONAL-ICOSITETRAHE^ 

 DRONS. 



The faces of the tetrahedral Trigonal-icositetra- 

 hedrons, Figs. 25. 26., are scalene triangles. 



1. These forms have four solid angles, and six faces, all 

 of which are equiangular and digram mic. Those contained 

 by four faces, six in number, are situated above the 

 centres of the edges ; the more obtuse solid angles of six 

 faces, four in number, above the centres of the faces of the 

 tetrahedron, and the more acute solid angles formed by 

 the same number of faces, also four in number, correspond 

 to the solid angles of this form. 



2. There are three different kinds of edges in this form. 

 The longest join those solid angles of six faces which are 

 not similar to each other, the intermediate ones the more 

 acute, and the shortest the more obtuse of these solid angles 

 with those which are bounded by four faces. 



