. 121, 122. OF THE CONNEXION OF FORMS. 129 



sume, it corresponds to the face of a form of seve- 

 ral axes. 



We obtain or derive the forms of several axes from the 

 hexahedron, by considering the space limited by all those 

 faces which are homologous to the one whose situation has 

 been ascertained. 



Hence there will exist as many different kinds of forms 

 of several axes, as there are possible situations of the 

 moveable plane, and no more ; and we obtain, therefore, 

 the complete number of these forms, whilst at the same time 

 every form is excluded which does not belong to this as- 

 semblage. 



In the preceding paragraphs 57 77> we have met with 

 more than seven forms of several axes. Those which are 

 not immediately produced according to the present consi- 

 deration, are nevertheless contained in its results, the 

 mode of which will be explained in the paragraphs 128 

 134. 



. 121. THE OCTAHEDRON. 



In the first situation the moveable plane is the 

 face of the Octahedron (. 59.). 



Of the forty-eight faces which are moveable round the 

 eight solid angles of the hexahedron, every six conti- 

 guous to one of these solid angles coincide in one and the 

 same plane, perpendicular to a rhombohedral axis of the 

 form (. 59. 2.). 



. 122. THE DODECAHEDRON. 



In the second situation the moveable plane is 

 the face of the Dodecahedron (. 63.). 



A pair of faces from every solid angle of the hexahedron 

 coincides with another pair of faces contiguous to an adja- 



