. 157. OF COMBINATIONS. 207 



dron, and the first variety of the digrammic tetragonal-ieo- 

 sitetrahedrons, to be considered as a rhombohedral combina- 

 tion, of which the hexahedron is the fundamental form 

 R = 90. The octahedron is consequently =11 co. 

 R + 1 ; the dodecahedron = 11 1. P + co ; and the di- 

 grammic tetragonal-icositetrahedron = 11 2. (P I) 3 . 

 R + co. The entire tessular combination expressed as 

 a compound form of the rhombohedral system, is therefore 

 = R co. R _ 2. R 1. R. (P I) 3 . R + 1. R + co. 

 P -f co. It may here be observed, that besides other forms, 

 this combination contains four consecutive members of one 

 series of rhombohedrons, one of which is R = 90. The 

 designation of this compound form, as belonging to the tes- 

 sular system, is : H. O. D. Ai. 



It is evident that this may likewise yield a method of 

 finding the dimensions of the different varieties of such 

 forms, as possess faces not perpendicular to any axis, of 

 icositetrahedrons, of tetracontaoctahedrons, &c. 



. 157. SEMI-TESSULAR COMBINATIONS. 



A combination of the tessular system assumes a 

 Semi-tessular Character, if it contains one or more 

 Halves. The semi-tessular combinations must far- 

 ther be distinguished into semi-tessular combina- 

 tions of parallel faces, and of 'inclined faces ', accord- 

 ing to the kind of halves which they contain (. 128.). 



Among those binary semi-tessular combinations, which 

 contain only one Half, there are two in particular deserving 

 of notice. The first of them is the combination of the octahe- 

 dron with one of the hexahedral pentagonal-dodecahedrons. 

 The faces of the octahedron appear as equilateral triangles 

 in the place of the rhombohedral solid angles of the penta- 

 gonal-dodecahedron. If all the faces of the combination 

 become triangles, the form produced is contained under 



