TL;DR
This paper extends previous work on 2D max/min puzzles to 3D, finding the smallest regular tetrahedron that contains various regular polyhedra, advancing geometric containment problems.
Contribution
It introduces a 3D analogue to prior 2D max/min puzzles, analyzing containment of regular polyhedra within the smallest possible regular tetrahedron.
Findings
Identifies minimal tetrahedra containing cubes, octahedra, icosahedra, and dodecahedra.
Extends geometric containment concepts from 2D to 3D.
Provides bounds and constructions for minimal enclosing tetrahedra.
Abstract
In the previous paper, Max/Min Puzzles in Geometry III, we searched for the smallest area triangle which contained a regular unit polygon (Square, Pentagon, Hexagon). In this paper we will work in 3-dimensions, and search for the smallest regular Tetrahedron which contains a regular unit polyhedron (Cube, Octahedron, Icosahedron, Dodecahedron).
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · Advanced Mathematical Theories