simplex
Sign in to saveAlso known as hypertetrahedron
alt=From left to right: a point (marked 0), a line (marked 1), a triangle (marked 2), and a tetrahedron (marked 3).|thumb|The four simplexes that can be fully represented in 3D space.
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- Commons category
- Simplex
- Schläfli symbol
- {3ⁿ⁻¹}
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~35 min read
Article
24 sectionsContents
- History
- Elements
- Symmetric graphs of regular simplices
- Standard simplex
- Examples
- Increasing coordinates
- Projection onto the standard simplex
- Corner of cube
- Cartesian coordinates for a regular {{mvar|n}}-dimensional simplex in '''R'''<sup>''n''</sup>
- Geometric properties
- Volume
- Dihedral angles of the regular ''n''-simplex
- Simplices with an "orthogonal corner"
- Relation to the (''n'' + 1)-hypercube
- Topology
- Probability
- Aitchison geometry
- Compounds
- Algebraic topology
- Algebraic geometry
- Applications
- See also
- Notes
- References
alt=From left to right: a point (marked 0), a line (marked 1), a triangle (marked 2), and a tetrahedron (marked 3).|thumb|The four simplexes that can be fully represented in 3D space.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell.