The ancient Greeks gave the polyhedron a name by the number of faces. “Hexa” means six, “hedra” means a face (Hexahedron is a body with six faces).
The polyhedron belongs to regular polyhedra and is one of the five Platonic solids.
The face of a polyhedron is a square. Each of the four angles is 90 degrees.
The number of sides at the face - 4
The number of edges adjacent to each vertex - 3
Total number of vertices - 8
Total number of edges - 12
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 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:
One can specify the following mathematical characteristics in each of the five Platonic solids: 1....