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 fringe 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 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 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:
The ancient Greek philosopher Plato associated the hexahedron with the - ground, one of the basic "earthly" elements, so we chose a brown color to build a model of this regular polyhedron.
The figure shows a hexahedron net: