Abstract
We describe the geometry of an arrangement of 24-cells inscribed in the 600-cell. In Section 7 we apply our results to the even unimodular lattice E8 and show how the 600-cell transforms E8/2E8, an 8-space over the field F2, into a 4-space over F4 whose points, lines and planes are labeled by the geometric objects of the 600-cell.
Communicated by: W. M. Kantor
Funding: The authors were supported by the Student Research Fellowship program at McDonogh 35 High School in New Orleans.
Acknowledgements
The authors thank Professor Cathy Kriloff of Idaho State University for suggesting they use the techniques they developed in [1] to study H3 (and H4) symmetry, they thank their advisor Rich Margolin for several helpful conversations, and they thank the referee for a number of suggestions that improved the text and corrected the terminology of this paper.
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