( 692 ) 



use of the annotation <({/>,</) formerly introduced {Verhandelin<ien, 

 vol. IX, N". 7, page 17) then the central section is a poly tope 



4p/5(-, -| and we find, oniittijig the length of axis 4l/5 alike 



for all sections, for the transition forms and \\w, intermediary forms 

 described above the following rhombotope symbols: 



1 f 1 



10 ' ' 



10 



5 

 10 



M. 



M.= 



— .1/5 = 

 10 ' 



10 



M. 



1 3 



3 5 



Ï ''' = {'' Ï 



2 n 2 



5 -'^' = (4' 4 



3 /2 3 

 5 ''^ = [V 4 



4 /3 4 



3. The second jmrt of the question, viz. how the intersecting space 

 Sp, affects the other measure-polytopes can now be answered by 

 means of analytical geometry as well as by descriptive geometry. 



With reference to the system of coordinates assumed above the 

 centres and vertices of all cells Alf^ of the net have all nothing but 



integers as coordinates, the centres only evan integers, the vertices 

 only odd ones. From this follows in genei-al that the distances from 



the centres to the central space S ,/■• = are multiples of tifth parts 



1 



of the diagonal, those of the vertices to the same space odd multiples 



of tenth parts of the diagonal. Iji this way a space of intersection 



2 xi = }) in general furnishes live different sections of which the 

 1 



1 

 fractions placed before M^ ditFer respectively - . If the space of 



5 



intersection passes through a vertex we find the transition sections; 

 if it passes though a centre we find the intermediary forms. 



We arrive at the same result by diagram 2. If we allow the same 

 space S[)^ bisecting perpendicularly the diagonal P' Q of the central 

 cell to intersect the right adjacent cell with the diagonal PQ', 

 then the segment QO cut from the diagonal of the central cell passes 



