(1) Definition: A revolving body surrounded by a straight line with one side of a rectangle and rotating with the other three sides is called a cylinder. The axis of rotation is called the axis of the cylinder; The circular surface formed by the rotation of the edge perpendicular to the axis is called the bottom surface of the cylinder; The surface that rotates parallel to the edge of the shaft is called the side of the cylinder.

(2) Representation of cylinders: cylinders are represented by letters representing their axes.

Step 2: Cone

(1) A body of revolution surrounded by a straight line with one right side of a right triangle as the axis of rotation and the other two sides rotating is called a cone.

(2) Representation of a cone: A cone is also represented by letters representing its axis.

3. truncated cone

Definition: cut the cone with a plane parallel to the bottom of the cone, and the part between the bottom and the section is called truncated cone.

Step 4: Ball

(1) The rotation body formed by taking the straight line with the diameter of the semicircle as the rotation axis and the semicircle turning once is called a spherical surface, which is called a ball for short. The center of the semicircle is called the center of the ball, the radius of the semicircle is called the radius of the ball, and the diameter of the semicircle is called the diameter of the ball.

(2) Spherical distance: the length of the shortest connecting line between two points on the sphere is the length of the bad arc between two points of the great circle passing through these two points. We call this arc length the spherical distance between two points.

(2) Representation of the ball: The ball is usually represented by letters representing the center of the ball.

5. Prism

(1) Definition: If two faces of a polyhedron are parallel to each other, the other face is a quadrilateral, and the common sides of every two adjacent quadrilaterals are parallel to each other, the geometry enclosed by these faces is called a prism. These two parallel faces are called the bottom face of the prism, and the other faces are called the side faces of the prism. The common edge of two faces is called the edge of a prism, the common edge of two faces is called the side edge of a prism, and the distance between two bottom faces is called the height of a prism.

(2) Representation of the prism: it is represented by letters corresponding to the upper and lower bottom surfaces, or by letters at both ends of the diagonal.

(3) Classification of prisms: A prism whose side is not perpendicular to the bottom surface is called an oblique prism, a prism whose side is perpendicular to the bottom surface is called a straight prism, and a straight prism whose bottom surface is a regular polygon is called a regular prism.

(4) the nature of the prism:

① All sides of a prism are parallelograms, all sides are equal, all sides of a straight prism are rectangles, and all sides of a regular prism are congruent rectangles.

(2) The two bottom surfaces of the prism and the sections parallel to the bottom surfaces are congruent polygons with parallel corresponding sides.

③ The cross sections of two non-adjacent sides of a prism are parallelograms.

6. pyramids

(1) Definition: If one face of a polyhedron is a polygon and the other faces are triangles with a common vertex, then the polyhedron is called a pyramid. A triangle with a common vertex in the pyramid is called the side of the pyramid, and the remaining polygons are called the bottom or bottom of the pyramid. The common side of two adjacent sides is called the side of the pyramid and the common side of each side.

(2) The representation of pyramid: vertex-bottom, or vertex-bottom diagonal.

(3) Classification of pyramids: According to the number of sides of the polygon at the bottom of the pyramid, it is called triangular pyramid, quadrangular pyramid, pentagonal pyramid, etc. The base is a regular polygon, and the projection of the vertex on the base is the center of the base, so the pyramid is called a regular pyramid. There are regular triangular pyramids and regular quadrangular pyramids accordingly.

(4) The nature of the pyramid: If the pyramid is cut by a plane parallel to the bottom, the cross section is similar to the bottom, and the ratio of the cross section area to the bottom area is equal to the square of the distance from the apex to the cross section and the height ratio of the pyramid.

7. Prism

(1) Definition: When a plane parallel to the bottom of a pyramid is used to cut the part between the bottom and the section, a polyhedron is called a pyramid. The bottom surface and cross section of the original pyramid are called the lower bottom surface and the upper bottom surface of the pyramid respectively.

(2) Representation of prism: Like prism, it is represented by letters corresponding to the top and bottom surfaces.