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Hexahedron (Cube)

cube

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).

Therefore, to the question “what is a hexahedron?”, We can give the following definition: “A hexahedron is a geometric solid of six faces, each of which is a regular quadrilateral (square)”.

The polyhedron belongs to regular polyhedra and is one of the five Platonic solids.

 

Kub forma grani The face of a polyhedron is a square. Each of the four fringe is 90 degrees.

Characteristics of the hexahedron (cube)

kub 2

The number of sides at the face - 4

kub 3Total number of faces - 6
Face shape square
Число рёбер примыкающих к каждой вершине

The number of edges adjacent to each vertex - 3

Общее число вершин куба

Total number of vertices - 8

Общее число ребер куба

Total number of edges - 12

параллельные ребраEach 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.
перпендикулярные ребра
перпендикулярные ребра

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.

 

скрещивающиеся ребра

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.

 

параллельные грани

Number of pairs of parallel faces - 3

Расстояние между противоположными рёбрами

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

Kub form1

,where "a" is the side length

Длина диагонали куба

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

Kub form2

центр симметрии кубаThe 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:

ось вращения куба
ось вращения куба
разрез куба плоскостью симметрии

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

ось симметрии куба
ось симметрии куба
ось симметрии куба
ось симметрии куба
ось симметрии куба
ось симметрии куба

The cube has 9 planes of symmetry

  Three planes pass through the center parallel to the faces

 

разрез куба плоскостью симметрии
разрез куба плоскостью симметрии
разрез куба плоскостью симметрии

Six planes pass through the center diagonally

разрез куба плоскостью симметрии
разрез куба плоскостью симметрии
разрез куба плоскостью симметрии
разрез куба плоскостью симметрии
разрез куба плоскостью симметрии
разрез куба плоскостью симметрии

1 kub opis

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

 

R kub

    where "a" -  is the side length.

2 kub vpis

The sphere can be inscribed inside the cube.

The radius of the cube's inscribed sphere

 

r1 kub

kub 1

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:

cube form3

3 kub s

4 kub s

Surface area of the cube

The surface area of the cube can be represented in the form of the net area.

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

 

S kub

5 kub v

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

V kub

Cube nets

The cube can be made by yourself. Paper or cardboard is the most suitable option. For the assembly will require paper net - a single part with the lines of the folds.

plato 1 lg
Choose a color for a polyhedron.

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:

 

ris2 geksahedronTo build a model, you can download a net in pdf format and print it on an A4 sheet:
- if you print on a color printer - color net (pdf)
- if you use color cardboard for assembly - net (pdf)

Video. Cube from the set "Magic Edges"

You can make a model of hexahedron (cube) using the parts for assembly from the set "Magic Edges".

12 obl 400

Video. Build a polyhedron from a set:

Video. Rotation of the finished polyhedron:

Video. Rotation of all regular polyhedra

 

 

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