( 548 ) 
ve : we? S We B Eee LE 7e d 22 
’ 6 ] 6 ay 6 Va ’ Ti 5 6 an . 
Sections normal to OF,, = OK,. 
To the five polyhedra presenting themselves here — see the first 
column of the third part of plate IT — correspond below to the right 
1 + 2 
the fractions 0, —,...,—, above to the left the fractions —, 
8 8 12 
3 6 
12’ DR) 12 
Here too the problem of the determination of the section of the 
eightcell has lost one dimension, these sections being prisms with a 
height 2, the bases of which are sections of a cube, this time normal 
to a diagonal. Here too it is desirable to determine independently 
the faces of the sections of the inscribed C,, situated in the limiting 
faces of these prisms. To this end we have to revert to the diagrams 
5e, Db, 5° and to replace the series of parallel lines representing 
the traces of the intersecting planes normal to the planes of the 
diagrams made up in the supposition of the intersecting space (2,1,1,0) 
by those which are connected with the simpler supposition (1,1, 1,0). As 
the new diagrams 5? and 5° become equal to one another, the new 
series of parallel lines have only been indicated — by dotted lines 
— in the diagrams 5% and 5’. So we find — entirely in the manner 
explained above — the section wv of the octahedron in the equi- 
angular semiregular hexagon fx forming the end planes, the section 
t’u’v’ w’ in the rectangle s’ 7’ forming the three lateral faces of the 
prismal section corresponding to the fraction ay ee easily get 
— once more in the same manner as above — by means of the 
data of plate Il the total boundary of each of the five sections of C 
The forms obtained in this way possess the same characteristic 
properties as those of the preceding group, an axis J/N with the 
period 3 and four planes of symmetry for the excentric sections, an 
axis with the period 6 and seven planes of symmetry for the central 
section. We can only record this difference that here the line MN 
is an axis for the sections of the C,, and those of the circumscribed 
C’, together, and that its length within the polyhedra always remains 2. 
Sections normal to OF,, = (3,1,1,1) C,. 
Here we find — see the second column of the third part of plate II 
a derd ™ 
