Four-dimensional tetrahedron (also called hyper-tetrahedron) is formed by connecting five points in different spaces. Three-dimensional coordinate system is three perpendicular lines, but its projection on the plane has one line that is not perpendicular to the other two. Then according to the definition, the coordinate system in four-dimensional space is composed of four mutually perpendicular straight lines (not in the same space), so it should be inferred that one line projected in three-dimensional space is not perpendicular to the other three.

If four points and every three points in the two-dimensional coordinate system are connected into a triangle, the projection of the three-dimensional tetrahedron in two dimensions can be obtained. Similarly, if five points and every four points in the three-dimensional coordinate system are connected into a tetrahedron, the projection of the four-dimensional tetrahedron (super tetrahedron) in the dimension can be obtained.

Extended data

Hypercube, in geometry, a four-dimensional cube is a four-dimensional analogy of a cube. A four-dimensional cube is to a cube what a cube is to a square. A four-dimensional cube is a four-dimensional convex polyhedron with eight cubic cells. Cubes with dimensions greater than 3 are hypercubes or measure polyhedrons. Point-to-line, line-to-line, face-to-body, cube-to-hypercube.

Four-dimensional basic figure is four-dimensional tetrahedron (super tetrahedron), five of which are not in the same space? Five points on the plane are connected with each other. But its projection in three-dimensional space is formed by connecting five points in the same space. Thus, the projection of four-dimensional tetrahedron (super tetrahedron) in three dimensions is obtained.

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