On Extremal Volume Projections of the Simplex and the Cube
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908788824473600 |
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| author | Pandis, Christos |
| author_facet | Pandis, Christos |
| contents | Let $Δ_n$ and $Q_n$ denote the regular $n$-simplex of side length $\sqrt{2}$ embedded in $\mathbb{R}^{n+1}$ and the volume one cube in $\mathbb{R}^n$, respectively. We derive a closed-form formula for the hyperplane volume projections of $Δ_n$, which also yields the directions achieving the extremal volume. Moreover, we revisit the problem of extremal planar projections of $Q_n$. In addition, we present generalizations within the framework of $L_p$-projection bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18436 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Extremal Volume Projections of the Simplex and the Cube Pandis, Christos Metric Geometry Functional Analysis Let $Δ_n$ and $Q_n$ denote the regular $n$-simplex of side length $\sqrt{2}$ embedded in $\mathbb{R}^{n+1}$ and the volume one cube in $\mathbb{R}^n$, respectively. We derive a closed-form formula for the hyperplane volume projections of $Δ_n$, which also yields the directions achieving the extremal volume. Moreover, we revisit the problem of extremal planar projections of $Q_n$. In addition, we present generalizations within the framework of $L_p$-projection bodies. |
| title | On Extremal Volume Projections of the Simplex and the Cube |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2601.18436 |