Plane Sections of Symmetric Tetrahedral Cones
Inverse Fibers, Poncelet 3-Porisms, Phase Transitions, and Triangle Loci
Abstract
We study the shapes of triangles cut from a one-parameter family of symmetric trihedral cones, equivalently from tetrahedra whose equilateral base is allowed to recede arbitrarily far. The work develops the inverse problem, Poncelet 3-porisms, the phase-transition structure, and the triangle-center loci arising from these sections.
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