Abstract
In this paper, we consider two classes of polyhedra. One is the class of polyhedra of maximal volume with n vertices that are inscribed in the unit sphere of R 3. The other class is polyhedra of minimal volume with n vertices that are circumscribed about the unit sphere of R 3. We construct such polyhedra for n up to 30 by a computer aided search and discuss some of their properties.
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Croft, H.T., Falconer, K.J., Guy, R.K.: Unsolved Problems in Geometry. Springer, Heidelberg (1995)
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© 2003 Springer-Verlag Berlin Heidelberg
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Mutoh, N. (2003). The Polyhedra of Maximal Volume Inscribed in the Unit Sphere and of Minimal Volume Circumscribed about the Unit Sphere. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_22
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DOI: https://doi.org/10.1007/978-3-540-44400-8_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20776-4
Online ISBN: 978-3-540-44400-8
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