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Answer by Blue for Maximum volume of tetrahedron with given face areas
Given four face-areas, the tetrahedron of maximum volume is the one in which opposite edges are perpendicular.(I call these "perfect" tetrahedra, although they are called "orthocentric" in the...
View ArticleAnswer by Dmitry Baksheev for Maximum volume of tetrahedron with given face...
Ernst D. Krupnikov suggests the following lemma:If the four faces $a$, $b$, $c$, $d$, of a tetrahedron satisfy identity $a^2+b^2+c^2=d^2$, then the volume $V$ of the tetrahedron satisfies identity...
View ArticleMaximum volume of tetrahedron with given face areas
Everyone knows Heron formula for the area of a triangle as a function of its sides. Moving to three dimensions, what is the maximum volume of a tetrahedron with given four face areas $a$, $b$, $c$, and...
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