**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 parallel edges pairs 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 formula can determine the distance between the opposite edges, where "a" is the side length.

The formula can determine the length of the cube diagonal.

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 sphere's inner wall.

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 inscribed sphere

The sphere can be inscribed in a cube to touch the surface of all the edges of the cube.surface of all the edges of the cube. Such a sphere is called semi-inscribed in a cube.

The formula can determine the radius of the semi-written sphere:

**The surface area of the cube.**

The surface area of a cube can be represented as a shape net area.

The cube surface area can be defined as the area of one of the cube's sides. This is the area of a regular quadrilateral (square), multiplied by 6. Or use the formula:

The following formula determines the volume of the cube:

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