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**## Characteristics of the hexahedron (cube)

The number of sides at the face - 4

Total number of faces - 6

Face shape square
The number of edges adjacent to each vertex - 3

Total number of vertices - 8

Total number of edges - 12

Each edge (red) has three parallel edges (blue).

The number of pairs of parallel edges can be determined by multiplying the total number of edges by 3.

In a cube, 18 pairs of parallel edges.
Each edge (red) has 8 edges perpendicular to it (blue). To determine the number of pairs of perpendicular edges, you can multiply the total number of edges by 8 and divide by 2.

In total, the cube has 48 pairs of perpendicular edges.

Each rib (red) has 4 ribs intersecting it.

Determine the number of pairs of crossed edges by multiplying the total number of edges by 4 and dividing by 2.

In total, the cube has 24 pairs of intersecting edges.

Number of pairs of parallel faces - 3

The distance between the opposite edges can be determined by the formula

,where "a" is the side length

The length of the cube diagonal can be determined by the formula

The cube has a center of symmetry.
The cube has 9 axes of symmetry.

Three axes of symmetry are straight lines passing through the center of the parallel faces of the cube:

The six axes of symmetry are the direct connecting centers of the opposite edges of the cube:

The cube has 9 planes of symmetry

Three planes pass through the center parallel to the faces

Six planes pass through the center diagonally

A cube can be placed in a sphere (inscribed), so that each of its vertices will touch the inner wall of the sphere.

The radius of the described sphere of the cube

where "a" - is the side length.

The sphere can be inscribed inside the cube.

The radius of the cube's inscribed sphere

The sphere can be inscribed in a cube in such a way that it touches the surface of all the edges of the cube. Such a sphere is called semi-inscribed in a cube.

The radius of the semi-written sphere can be determined by the formula:

**Surface area of the cube**

The surface area of the cube can be represented in the form of the surface area shape net. The cube surface area can be defined as the area of one of the sides of the cube - this is the area of a regular quadrilateral (square), multiplied by 6. Or use the formula:

The volume of the cube is determined by the following formula:

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