1174 
1910 this Academy published a treatise of Mrs. A. Boone Storr: 
“Geometrical deduction of semiregular from regular polytopes and 
space fillings’. This treatise contains a method by which bodies 
having a certain kind of semiregularity may be derived from regular 
bodies, with application to any number of dimensions. The methods 
were essentially geometric; ScHoure resolved to give the analytical 
counterpart. The conception might seem simple, the execution 
proved to be very laborious. Many theorems had to be tested for 
spaces of more than three dimensions; we give the subdivision of 
each of the four published sections as a proof. A. Symbols of the 
coordinates. £4. The characteristic numbers. C. Extension numbers 
and truncation integers and fractions. DD. Expansion and contraction 
symbols. #. Nets of polytopes. #. Polarity. G. Symmetry, con- 
siderations of the theory of groups, regularity. The author’s analysis 
extends over four principal forms of polytopes and many difficulties 
in the consideration of spaces of more than three dimensions had 
to be conquered. 
The fifth section deals with polyhedrons deduced from icosahedron 
24? C C 
The author had to apply a method very closely connected with the 
geometrical generation of the bodies as a consequence of the impossi- 
and dodecahedron and the forms of S, deduced from C "ap, Gene 
bility of applying some of his former principles. The analysis of 
C,,. did not present insurmountable difficulties, but the number of 
characteristic numbers and coordinates belonging to C,,, and C,,, is 
very great. The reciprocity of C,,, and C,,, however allows to limit 
the considerations to C,,,. 
It has been already hinted that subdivision and results were 
found in Dr. Scnoure’s manuscript. The form was however very 
v 
120 600 
concise and a mark from his hand indicated some results he had 
not yet soundly tested. The text was in Dutch, a final redaction in 
English in harmony with the other sections was not yet begun. A 
general revision of the work which would have allowed the author 
to give to its methods that perfect unity at which he aimed, had 
not been made. 
Now this became the task of the editors, a task which had to be 
fulfilled with all the piety due to Scnourw’s memory. The author of 
this communication gave a first redaction in English. The great and 
laborious work however, consisting in the controlling and filling up 
of the characteristic numbers and coordinates and the ensuing final 
redaction is due to Dr. W. A. Wutrorr, whose kind collaboration 
made it possible to publish Scuournr’s last work, a collaboration 
which will be thankfully remembered. 
