The introduction of catching the ball is as follows:

The circumscribed sphere refers to the circumscribed sphere of space geometry. There are different definitions of circumscribed sphere for rotating body and polyhedron. The generalized understanding is that the sphere surrounds the geometry, and the vertex and cambered surface of the geometry are on this sphere. The vertices of a regular polyhedron are on the same sphere, which is called the circumscribed sphere of a regular polyhedron.

Details are as follows:

Point o is the intersection of two straight lines passing through the center of the circumscribed circle of the nonparallel plane of the polyhedron and perpendicular to the nonparallel plane; Point o is the intersection of three planes passing through the midpoint of non-parallel edges of polyhedron and perpendicular to these edges; Point O is the intersection of a straight line passing through the center of the circumscribed circle of a face and perpendicular to the plane ∑ of the circle and a plane passing through the midpoint of an edge that is not parallel to ∑ and perpendicular to the edge.

As follows:

The circumscribed sphere refers to the circumscribed sphere of space geometry. The circumscribed sphere and polyhedron have different definitions. The generalized understanding is that the sphere surrounds the geometry, and the vertex and cambered surface of the geometry are on this sphere.

The circumscribed radius of a quadrilateral: r circumscribed ball =(h-R circumscribed ball) +r circumscribed circle. A quadrilateral is a closed figure composed of four triangles and a quadrilateral, while the bottom of a regular quadrilateral is a square, and the four triangles are congruent triangles and isosceles triangles.

The circumscribed sphere refers to the circumscribed sphere of space geometry. There are different definitions of circumscribed sphere for rotating body and polyhedron. The generalized understanding is that the sphere surrounds the geometry, and the vertex and cambered surface of the geometry are on this sphere. The vertices of a regular polyhedron are on the same sphere, which is called the circumscribed sphere of a regular polyhedron.

A regular tetrahedron with a side length of a can be regarded as a cube with a side length of (√2/2)a, and the diameter of its circumscribed sphere is √3 times the side length of the cube.

Mathematically, the formula of circumscribed sphere of arbitrary tetrahedron refers to the formula for calculating the surface area and volume of sphere according to the lengths of three sides of tetrahedron (that is, side lengths A, B and C).