TERMINOLOGY, . 12G. 



which are contiguous to the same solid angle, the other two 

 to the adjacent ones. The faces are four-sided ; and on ac- 

 count of the two kinds of edges which the form contains, 

 it is a digrammic Tetragonal-icositetrahedron (. 74. 2.). 



The digrammic Tetragonal-icositetrahedrons may be con- 

 sidered as forms intermediate between the hexahedron and 

 the octahedron. For if the angle measuring the inclination 

 of the moveable plane to the axis AX becomes greater 

 than BAX, a digrammic Tetragonal-icositetrahedron will be 

 produced, and the varieties of this form will succeed each 

 other, till the angle just mentioned becomes = 90, when the 

 derived form is changed into the octahedron. The dimen- 

 sions of the different varieties, are dependent upon the 

 value of that angle. 



. 126. THE HEXAHEDRAL TRIGONAL-ICOS1TETRA- 

 HEDRON. 



In the sixth situation the moveable plane is the 

 face of a tiexaliedral Trigonal-icositetrdhedron 

 (. 71.). 



This icositetrahedron is produced by the coincidence of 

 two faces contiguous to adjacent solid angles. From every 

 edge of the hexahedron faces rise towards the prolongation 

 of the pyramidal axes, at which they form a solid angle of 

 four faces, intersecting each other at equal angles, while 

 the general aspect of the hexahedron is retained in the de- 

 rived form. The rhombohedral solid angles are equiangu- 

 lar, but they consist of two kinds of edges. 



Each of the faces of this form is intersected by three 

 other faces, of which one is contiguous to the same, and one 

 to an adjacent solid angle of the hexahedron, the third face 

 being common to both these solid angles. The faces of 

 this form are consequently triangular, and intersect each 

 other at equal angles in its pyramidal solid angles. The 

 form, therefore, will be a hexahedral Trigonal-icositetrahe- 

 dron. 



