16-cell

{{Infobox polychoron | Name=16-cell(4-orthoplex)| Image_File=Schlegel wireframe 16-cell.png| Image_Caption=Schlegel diagram(vertices and edges)| Type=Convex regular 4-polytope4-orthoplex4-demicube| Last=11| Index=12| Next=13| Schläfli={3,3,4}| CD= | Cell_List=16 {3,3} 25px| Face_List=32 {3} 25px| Edge_Count= 24| Vertex_Count= 8| Petrie_Polygon=octagon| Coxeter_Group=B4, [3,3,4], order 384D4, order 192| Vertex_Figure=80pxOctahedron| Dual=Tesseract| Property_List=convex, isogonal, isotoxal, isohedral, regular, Hanner polytope }} In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid.

It is the 4-dimensional member of an infinite family of polytopes called cross-polytopes, orthoplexes, or hyperoctahedrons which are analogous to the octahedron in three dimensions. It is Coxeter's \beta_4 polytope. The dual polytope is the tesseract (4-cube), 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.