16-cell

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the 16-cell is the <a href="/facts/Regular_convex_4-polytope/lFf8IH1C">regular convex 4-polytope</a> (four-dimensional analogue of a Platonic solid) with <a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli symbol</a> {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician <a href="/facts/Ludwig_Schl%C3%A4fli/mszJDaFn">Ludwig Schläfli</a> in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid [<a href="/facts/Sic/qB9MUUWF">sic</a>?] .
It is the 4-dimensional member of an infinite family of polytopes called <a href="/facts/Cross-polytope/erk0byF6">cross-polytopes</a>, orthoplexes, or hyperoctahedrons which are analogous to the <a href="/facts/Octahedron/G38q92xW">octahedron</a> in three dimensions. It is Coxeter's 
 
 
 
 
 β
 
 4
 
 
 
 
 {\displaystyle \beta _{4}}
 
 polytope.[4] The <a href="/facts/Dual_polytope/rkIHbmAf">dual polytope</a> is the <a href="/facts/Tesseract/tlqouBoU">tesseract</a> (4-<a href="/facts/Hypercube/q2mRPbIz">cube</a>), which it can be combined with to form a compound figure. The cells of the 16-cell are dual to the 16 vertices of the tesseract.

16-cell open-in-new

16-cell