Which Shape Has Four Vertices and Four Faces?


Quick Answer

A tetrahedron is a three-dimensional shape that contains four vertices, four faces and six edges. This Platonic solid is classified as a polyhedron, specifically a regular convex polyhedron. This indicates that all the four faces of a tetrahedron are equal in shape and size, with the same number of surfaces joined at each vertex.

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Full Answer

The Swiss mathematician Leonhard Euler devised a formula to illustrate the correlation between the numbers of faces, edges and vertices of most three-dimensional figures. The formula is given as X = V - E + F, where "V" denotes vertices, "E" indicates edges, "F" represents faces and "X" is the Euler characteristic. By plugging in the correct values in the case of a polyhedron, the relationship can be expressed as X = 4 - 6 + 4. The Euler characteristic is always equal to 2.

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