A torus in the hyperoctahedron
The hyperoctahedron is one of the six regular polytopes in dimension 4, it has 16 tetrahedra as faces of dimension 3. 8 of these tetrahedra form a torus. The figure shows this construction, taking as reference the description of the hyperoctahedron as a bipyramid, with vertices v and v', on an octahedron (shown in the figure): the solid torus is the union of the pyramid with vertex v (on the four faces in evidence on the left) with the pyramid of vertex v' (on the four faces in evidence on the right).
© matematita
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Hyperoctahedron (4D geometry)
