# Regular hexahedral

## Characteristics

The nipper has the following characteristics:

(1) The six-sided body has 8 top points, and each vertex is connected to three ribs.

(2) The nippeng has 12 ribs, each rib length equal.

(3) 6 faces there are 6 faces, each surface area is equal, the shape is exactly the same.

(4) Body diagonal of the positive hexahedron:

, where A is a long.

## surface area and volume

### surface area

Because all surfaces of the positive six somariums are equal, all squares are square, so the surface area of ​​the positive six somatostat

, In which A is the male surface of the positive hexahedral, and S is the surface area of ​​the positive hexahedral.

### Volume

The positive body belongs to a prismatic, the volume formula of the prism is equally applicable, that is, the volume = bottom area × height. Since the six faces of the niphedral body are equal, and all of them are square, the volume of the positive hexahedral = the diamond length × long.

Sets a positive surface of a positive body to a, then its volume:

.

## Related Concepts

### diagonal

For example, as shown in Figure 1, a positive cube ABCD-

For A,

(1) first take the face-to-plane angle of the bottom surface (as line segment AC in Fig. 1), calculate, the length of AB =

;

(2) This face-to-plane AC and it intersects the rib, which is perpendicular to the upper surface of the upper bottom surface

is a body-to-corner, depending on the ticking theorem, it can be obtained, the length of the body diagonal of the niphedral body =
.

### Units

(1) The length is 1 cm of the positive six-faced body, the volume is 1 cubic centimeter;

(2) diamond is 1 piece The niphedral, the volume is 1 cubic gearization;

(3) The length is 1 meter positive six, the volume is 1 cubic meter.

### ball radius

(1) Outer ball radius: radius r = half of the square diagonal of the square;

(2) Radius: The radius r = half of the square side of the square.

### Plane truncation

with a plane truncation, the following triangles, rectangular, square, five-sided, pentagonal, hexagon, positive hexagon, diamond , The trapezoid, the specific tip is as follows:

(1) triangle: a line within the range of a vertex within the diagonal of the opposing surface;

(2) Rectangle: After two opposing edges or a rib;

(3) square: parallel to one side;

(4) five-dimensional: over four edges and a vertex Or the point on the five ridges;

(5) hexagon: the point on the ridges;

(6) Sixth: the midpoint of the rib; / P>

(7) diamond: over relatively vertex;

(8) trapezoid: parallel to two faces.

## Expand Figure

The expansion of the six-sided body Figure 2 is as follows:

(1) 1, 4, 1:

(2 2, 3, 1:

(3) 2, 2, 2:

(4) 3, 3:

## Beautiful set

Theorem 1

Theorem 1: If the square edge is longer A, with the circular radius of the center is R, the circle is connected to the square with the square The square and four times of the length of the segment are all set.

(1) Inference 1.1: If the side length of the square ABCD is A, P is any point on its outer circle, then:

is the value.

(2) Introduction 1.2: If the side length of the square ABCD is A, P is any point on its inner cut circle, then:

(3) Introduction 1.3: If the n-shape (n = 2k) edge length is a, the circular radius of the center of the center is R, and the circle is arbitrary with the positive The square of the length of the N-shaped vertices The square of length is:

.

(4) Introduction 1.4: If the n-shape ((n = 4k) diagonal length is m, the circular radius of the center of the center is the center radius of R, then the circle Any point of the length of the length of the positive N-shaped vertices is set:

theorem 2

Theorem 2: If the frontal length of the active body is A, with the radius of the ball in which the ball is the ball is R, the squad is from the square of the length of the positive part of the positive body to:

(fixed value), four squares and:
(fixed value).

(1) Inference 2.1: If the prime of the prescription is A, Any point on the length of the pellet with the vertices of the square and the square of the length of the positive part of the positive body, and the four squares and "section> .

(2) inference 2.2: If the probe of the active body is A, the square of the push-to-race length of the positive part is anywhere in the square, and it is

, four squares and
.

Related Articles