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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. It is also called C16, hexadecachoron, or hexdecahedroid .
The analysis highlights Geometry, Overview and Symmetry constructions as prominent areas in the source structure around 16-cell.
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The extracted context around 16-cell shows recurring relationship patterns in the source. For example, 16-cell → Euclidean, Hence, One, R4, Schläfli, Together, Twenty-four Another extracted example is 16-cell → 4-dimensional cross polytope, regular convex 4-polytope, second in the sequence of 6 convex regular 4-polytopes, simple frame in which to observe 4-dimensional rotations, simplest regular polytope in which they occur. Use these groups to spot repeated connection types before inspecting the individual relationships.
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vertices regular edges orthogonal vertex three cells tetrahedral one two squares symmetry octahedron planes tetrahedra completely tetrahedron also great rotation
TTTA extracted 37 structured relationships around 16-cell. Examples in this analysis include 16-cell → Cells → 16 {3,3} and 16-cell → Coxeter group → B4, [3,3,4], order 384 D4, order 192. The table shows each extracted connection, where it came from and its confidence.
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| 16-cell | Cells | 16 {3,3} | 1.00 | infobox |
| 16-cell | Coxeter group | B4, [3,3,4], order 384 D4, order 192 | 1.00 | infobox |
| 16-cell | Dual | Tesseract | 1.00 | infobox |
| 16-cell | Edges | 24 | 1.00 | infobox |
| 16-cell | Faces | 32 {3} | 1.00 | infobox |
| 16-cell | Petrie polygon | octagon | 1.00 | infobox |
| 16-cell | Properties | convex, isogonal, isotoxal, isohedral, regular, Hanner polytope | 1.00 | infobox |
| 16-cell | Schläfli symbol | {3,3,4} | 1.00 | infobox |
| 16-cell | Type | Convex regular 4-polytope 4-orthoplex 4-demicube | 1.00 | infobox |
| 16-cell | Uniform index | 12 | 1.00 | infobox |
| 16-cell | Vertex figure | Octahedron | 1.00 | infobox |
| 16-cell | Vertices | 8 | 1.00 | infobox |
| 16-cell | is a | regular convex 4-polytope | 0.90 | text |
| 16-cell | is a | second in the sequence of 6 convex regular 4-polytopes | 0.90 | text |
| 16-cell | is a | simple frame in which to observe 4-dimensional rotations | 0.90 | text |
| 16-cell | is a | simplest regular polytope in which they occur | 0.90 | text |
| 16-cell | is a | 4-dimensional cross polytope | 0.90 | text |
The concept neighborhoods around 16-cell bring nearby vocabulary together. In this analysis, examples include Regular, Vertices and Three. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
For 16-cell, one of the stronger structural bridges in this analysis connects 16-cell with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
TTTA analyzes the structure around 16-cell to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Geometry, Overview & Symmetry constructions, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
Source: Wikipedia — 16-cell · EN edition · Analysis: TopicsToTalkAbout