Star polytopes and the Schläfli function f(\(\alpha\) ,\(\beta\) ,\(\gamma\) ) (Q923367)
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scientific article; zbMATH DE number 4169554
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Star polytopes and the Schläfli function f(\(\alpha\) ,\(\beta\) ,\(\gamma\) ) |
scientific article; zbMATH DE number 4169554 |
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Star polytopes and the Schläfli function f(\(\alpha\) ,\(\beta\) ,\(\gamma\) ) (English)
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1989
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The paper starts with a short discussion of the regular figures in the 3- and 4-dimensional euclidean spaces, including the Kepler-Poinsot polyhedra and the Schläfli-Hess polytopes. The consideration of the concept of density for the star-shaped polytopes leads to the computation of the volume of a spherical tetrahedron. The author provides here an exposition which fills some gaps in Schläfli's original treatment.
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regular figures
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Kepler-Poinsot polyhedra
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Schläfli-Hess polytopes
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density
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star-shaped polytopes
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volume
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spherical tetrahedron
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