A simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. It serves as the basic building block in geometric topology and algebraic topology, allowing for the construction of more complex shapes and spaces through their combinations. Simplices can be defined in various dimensions, where a 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron, with higher-dimensional simplices continuing this pattern.
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