. 124. 125. OF THE CONNEXION OF FORMS. 131 



monogrammic tetragonal-dodecahedron is divided into two 

 isosceles triangles, whose common base is the longer diagonal 

 of the rhomb. The triangles retain their isosceles figure, 

 though the angles may vary, till the moveable plane inter, 

 sects the axis of the form at an angle of 90. In this case, 

 all the faces contiguous to the same solid angle coincide in 

 a single plane, which is the face of the octahedron. All 

 possible varieties of octahedral Trigonal-icositetrahedrons 

 are therefore contained between the two forms just men- 

 tioned, and the dimensions of their varieties depend upon 

 the magnitude of the above mentioned angle. 



. 124. THE HEXAHEDRON. 



In the fourth situation, the moveable plane is 

 the face of tlie Hexahedron (. 58.). 



In this situation pairs of faces from all the four solid 

 angles A, B, C, C' coincide in a plane perpendicular to the 

 pyramidal axis (. 58. 3.). 



. 125. THE DIGRAMMIC TETRAGONAL-ICOSITE- 

 TRAHEDRON. 



In the fifth situation, the moveable plane is the 

 face of a digrammic Tctragonal-icositetrahedron 

 (. 74.). 



The pairs of faces from the angles A and B, and those 

 from the angles C and C', do not coincide, but they inter, 

 sect each other at equal angles in a determined point of the 

 lengthened pyramidal axis of the hexahedron. A solid 

 angle of three faces is produced at the point*A. The 

 edges which produce these two kinds of solid angles unite 

 with each other in the prismatic axes prolonged, and thus 

 produce solid angles, which contain likewise four faces, but 

 two different kinds of edges. 



Each face is intersected by four other faces, two of 



