( 691 ) 



opposite edges PQ, P' Q intersecting tlie diagonal P'^ has been taken 

 as plane of projection. The projection of M^^ on this plane is the 



(^ C P A. 



Fig. 2. 



rectangle PQQP with edges PQ = 2, PP' = 4, which is divided 

 by three lines parallel to PQ into four equal rectangles. The inter- 

 secting space Sp^ passing through the centre stands according to the 

 perpendicular /, erected in O on the diagonal PQ, normal to the plane of 

 projection. If we suppose {Proceedhvjs, page 491) a few measure- 

 polytopes M^-^\ which are laid against each other in the direction 



of the edge PQ on either side, to be united to a prism of which 

 the basis is an }Pp and the edges normal to OA have the direction 



PQ, then the section of the space Sp^ through (J with this prism 

 is a rliombotope Rli^ of which AA' — with a length of 4 1/5 — 

 represents the axis with the period 4. Comparison of this rhombotope 

 with the measure polytope 3/(2 of J/(|) lying in the space Sp^ per- 

 pendicular according to m on the plane of projection shows us 

 that the rhombotope can be obtained by stretching this polytope 

 M^^) in the direction of the diagonal CC' to an amount of O A : (>6= 1/5. 



This rhombotope is truncated perpendicularly by the spaces Sp^ 

 projecting themselves in the points of intersection Z>, B' of the axis 

 AA' with the sides PP , QQ' of the rectangle. If again we make 



47* 



