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XIX.—Description of a Projection-Model of the 600-Cell in Space of Four Dimensions

Published online by Cambridge University Press:  15 September 2014

D. M. Y. Sommerville
D. M. Y. Sommerville
Affiliation:
University of St Andrews
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Extract

§ 1. In 1880 Stringham proved that in space of four dimensions there exist six and no more regular rectilinear figures, whose boundaries are regular polyhedra. The same result was arrived at independently by Hoppe in the following year. In 1883 Schlegel gave an extensive investigation of the same problem, and constructed projection-models of the six regular figures, which were exhibited at the Magdeburg meeting of the Society of German Naturalists in 1884. This series of models was published by the firm L. Brill of Darmstadt and is obtainable from their successors, Martin Schilling in Leipzig.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 34 , 1914 , pp. 253 - 258
Copyright
Copyright © Royal Society of Edinburgh 1914

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References

page 253 note 1 “Regular Figures in n-dimensional Space,” Amer. J. Math., 3, 1–14.

page 253 note 2 “Regelmässige linear begrenzte Figuren von vier Dimensionen,” Arch. Math., Leipzig, 67, 29–44.

page 253 note 3 “Theorie der homogenen zusammengesetzten Raumgebilde,” Halle, , Nova Ada Acad. Leop., 44, 343–459Google Scholar.

page 254 note 1 “Regelmässige Schnitte und Projectionen des Hundertzwanzigzelles und Sechshundertzelles im vierdimensionalen Raume,” Amsterdam, Verh. K. Akad. Wet. (1e. Sect.), II. No. 7 (1894).