( 884 ) 



a regular octahedron, increases in size from a point, the centre of 

 the cube, to the inscribed octahedron with edge 2 \ 2 and then it 

 passes through the same stadia in inverse order. Of the three diagrams 

 the second represents an intermediate stadium, in which the edge of 

 the octahedron is \ / 2. 



b. Inclined cells. If the point of intersection of the intersecting 



space normal to the axis ( ^l\ Xf> of C\g * with this axis describes this 



axis completely, the section with the bodily circumscribed C\ remains 



a cube with edge two, whiJsl the section with the inscribed Gig ' > 

 always a tetrahedron truncated at the vertices and at the edges, trans- 

 forms itself from a right tetrahedron to a left one in the manner shown 

 by the five diagrams. In the third of the live we recognize the 

 semiregular body (with regular faces forming the combination of 

 cube and octahedron in equilibrium, whilst the form represented 

 b\ the second and the fourth show how this combination is formed 

 out of the right tetrahedron and passes into the left one 1 ). 



Sections normal to 0F 6 . 



a. Erect cells. Here a difference arises with respect to the fraction 

 indicating the position of the intersecting space, according as the line 

 through O normal to the intersecting space is considered either as 



an axis OK lt of the inscribed C ie ~' or as an axis OF s of the 



circumscribed 6 s . Therefore to each of the three diagrams presenting 

 themselves here correspond two fractions, one below at the righthand 

 side referring to the axis OK xt , another above at the lefthand side 

 referring to the axis 0F 8 . If the point of intersection of the inter- 

 secting space with the axis OF H of C» describes this axis completely, 

 the height of the rectangular parallelopipedon forming the section 



with C 8 , the base of which is a square with side four, increases 

 from nought to 4|/2 and then again decreases to nought. But only 

 at the moment that this height is increased to 2 I 2 does the polarly 



inscribed 6 ie begin to be cut. So we find in the three cases, where 



] ) For the sake of clearness the limiting elements of the section of the cell C' 1G 

 situated in the faces of the section of the enveloping box C 8 have been brought 

 to the fore by indicating the vertices situated in all the faces of that envelope as 

 black points, and by shading the faces of the section of the cell C 16 situated in 

 visible faces of that envelope. 



