Tetrahedrons & Octahedrons

The yellow triangles outline one of eight faces
of the octahedron within every tetrahedron.

The yellow triangles: One of the eight faces of an octahedron in the center of every tetrahedron and with a center point.

It all starts with sphere stacking and packing. More on stacking. Several pages are linked to this page. To return, the URL for this page is: https://81018.com/tot-2/ You can always use your “Back” button (top left arrow) within this desktop window.

Observe the octahedron. Many students find it difficult at first. Do you see where the heavy dark lines converge just below the lighter yellow horizontal line. Do you see that center tetrahedron with the two heavy dark lines (black and a very dark blue)? In your mind’s eye follow all those edges back inside to centerpoint of the larger octahedron and the largest tetrahedron pictured.

Also, visit the image on this page, as the octahedron game and the tetrahedral-octahedral gap.

Tetrahedral studies: We were fortunate that these perfect octahedrons and tetrahedrons were precision- engineered in and around the year 1998. Those first plastic models had multiple applications as math manipulatives to enhance studies and ask “What if?” questions within biology, chemistry (Also, see Shechtman, Lagarias & Zong) and structural engineering. There’s even a decorative arts application as a novelty picture frame.