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A k-simplex is a k-dimensional object formed by taking $k+1$ vertices and filling in all the space between them, which is known as the convex hull of those vertices.

Conditions: The dimension index k is a non-negative integer.; The construction involves $k+1$ vertices.

A k-simplex is a k-dimensional object formed by taking $k+1$ vertices and filling in all the space between them, which is known as the convex hull of those vertices.

Conditions: The dimension index k is a non-negative integer.; The construction involves $k+1$ vertices.