![]() It is one of the five regular Platonic solids, which have been known since antiquity. 3.5 A law of sines for tetrahedra and the space of all shapes of tetrahedraĪ regular tetrahedron is a tetrahedron in which all four faces are equilateral triangles.3.3 Properties analogous to those of a triangle.3.1.1 Heron-type formula for the volume of a tetrahedron.1.5 Cross section of regular tetrahedron.1.4 Orthogonal projections of the regular tetrahedron.1.3 Isometries of the regular tetrahedron.1.1 Coordinates for a regular tetrahedron.įor any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's faces. Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". ![]() The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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