Truncating edges down to points produces the as a rectified tetahedron | A regular tetrahedron can be embedded inside a in two ways such that each vertex is a vertex of the cube, and each edge is a diagonal of one of the cube's faces |
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that also includes a description of a "rotating ring of tetrahedra", also known as a |
Unlike the case of the other Platonic solids, all the vertices of a regular tetrahedron are equidistant from each other they are the only possible arrangement of four equidistant points in 3-dimensional space.
2This applies for each of the four choices of the base, so the distances from the apexes to the opposite faces are inversely proportional to the areas of these faces | Kahan, "What has the Volume of a Tetrahedron to do with Computer Programming Languages? The of a regular tetrahedron correspond to half of those of a cube: those that map the tetrahedra to themselves, and not to each other |
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