16-cell
Four-dimensional analog of the octahedron / From Wikipedia, the free encyclopedia
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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.[1] It is also called C16, hexadecachoron,[2] or hexdecahedroid [sic?] .[3]
16-cell (4-orthoplex) | |
---|---|
Type | Convex regular 4-polytope 4-orthoplex 4-demicube |
Schläfli symbol | {3,3,4} |
Coxeter diagram | |
Cells | 16 {3,3} |
Faces | 32 {3} |
Edges | 24 |
Vertices | 8 |
Vertex figure | Octahedron |
Petrie polygon | octagon |
Coxeter group | B4, [3,3,4], order 384 D4, order 192 |
Dual | Tesseract |
Properties | convex, isogonal, isotoxal, isohedral, regular, Hanner polytope |
Uniform index | 12 |
It is the 4-dimesional 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 polytope.[4] 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.