Simplex

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5. The standard n-simplex is the set ${\displaystyle \Delta _{n}}$ of points ${\displaystyle x=(x_{0},\dots ,x_{n})\in [0,1]^{n}}$ for which ${\displaystyle \sum _{i}x_{i}=1}$. For example, the standard 3-simplex is the shape of the corner of a cube if it is sliced off at an angle to produce a solid with three similar triangular faces (parts of the sides of the cube) and one larger, equilateral triangular face.