Editing Tetrahedral number (section)

== Geometric interpretation ==

Tetrahedral numbers can be modelled by stacking spheres. For example, the fifth tetrahedral number ({{math|''Te''<sub>5</sub> {{=}} 35}}) can be modelled with 35 [[billiard ball]]s and the standard triangular billiards ball frame that holds 15 balls in place. Then 10 more balls are stacked on top of those, then another 6, then another three and one ball at the top completes the tetrahedron.

When order-{{mvar|n}} tetrahedra built from {{math|''Te''<sub>''n''</sub>}} spheres are used as a unit, it can be shown that a space tiling with such units can achieve a densest [[sphere packing]] as long as {{math|''n'' ≤ 4}}.<ref>{{cite web|url=http://www.pisquaredoversix.force9.co.uk/Tetrahedra.htm|title=Tetrahedra|date=21 May 2000|archive-url=https://web.archive.org/web/20000521231622/http://www.pisquaredoversix.force9.co.uk/Tetrahedra.htm|archive-date=2000-05-21}}</ref>{{dubious|reason=diagram does not prove the statement|date=September 2018}}