Structural characteristics of 1, column, cone, platform and ball

(1) prism:

Definition: Geometry surrounded by two parallel faces, the other faces are quadrangles, and the common edges of every two adjacent quadrangles are parallel to each other.

Classification: According to the number of sides of the bottom polygon, it can be divided into three prisms, four prisms and five prisms.

Representation: Use the letter of each vertex, such as a five-pointed star, or use the letter at the opposite end, such as a five-pointed star.

Geometric features: the two bottom surfaces are congruent polygons with parallel corresponding sides; The lateral surface and diagonal surface are parallelograms; The sides are parallel and equal; The section parallel to the bottom surface is a polygon that is congruent with the bottom surface.

② Pyramid

Definition: One face is a polygon, and the other faces are triangles with a common vertex. These faces enclose a geometric figure.

Classification: According to the number of sides of the bottom polygon, it can be divided into three pyramids, four pyramids and five pyramids.

Representation: Use the letters of each vertex, such as a pentagonal pyramid.

Geometric features: the side and diagonal faces are triangles; The section parallel to the bottom surface is similar to the bottom surface, and its similarity ratio is equal to the square of the ratio of the distance from the vertex to the section to the height.

(3) Prism:

Definition: Cut off the part between the pyramid, the section and the bottom with a plane parallel to the bottom of the pyramid.

Classification: According to the number of sides of the bottom polygon, it can be divided into triangular, quadrangular and pentagonal shapes.

Representation: Use the letters of each vertex, such as a pentagonal pyramid.

Geometric features: ① The upper and lower bottom surfaces are similar parallel polygons; ② The side is trapezoidal; ③ The sides intersect with the vertices of the original pyramid.

(4) Cylinder:

Definition: Geometry surrounded by a surface formed by rotating one side of a rectangle with a straight line as the axis.

Geometric features: ① The bottom is an congruent circle; ② The bus is parallel to the shaft; ③ The axis is perpendicular to the radius of the bottom circle; ④ The side development diagram is a rectangle.

(5) Cone:

Definition: The geometric body surrounded by the surface formed by the circle rotates with the right angle side of the right triangle as the rotation axis.

Geometric features: ① the bottom is round; (2) The generatrix intersects with the apex of the cone; ③ The side spread diagram is a fan.

(6) frustum of a cone:

Definition: Cut the part between the cone, the section and the bottom with a plane parallel to the bottom of the cone.

Geometric features: ① The upper and lower bottom surfaces are two circles; (2) The side generatrix intersects with the vertex of the original cone; (3) The side development diagram is an arch.

(7) Sphere:

Definition: Geometry formed by taking the straight line where the diameter of the semicircle is located as the rotation axis and the semicircle surface rotates once.

Geometric features: ① the cross section of the ball is round; ② The distance from any point on the sphere to the center of the sphere is equal to the radius.