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arXiv · 1912.06156

The Geometry of $H_4$ Polytopes

Tomme Denney·Da'Shay Hooker·De'Janeke Johnson·Tianna Robinson·Majid Butler·Sandernisha Claiborne
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Abstract

We describe the geometry of an arrangement of 24-cells inscribed in the 600-cell. In $\S$7 we apply our results to the even unimodular lattice $E_8$ and show how the 600-cell transforms $E_8$/2$E_8$, an 8-space over the field $\bf{F}$$_2$, into a 4-space over $\bf{F}$$_4$ whose points, lines and planes are labeled by the geometric objects of the 600-cell.

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Tomme Denney, Da'Shay Hooker, De'Janeke Johnson, Tianna Robinson, Majid Butler, Sandernisha Claiborne. 2019-12-12. The Geometry of $H_4$ Polytopes. https://arxiv.org/abs/1912.06156

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