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# Cube

### Cube

This animation demonstrates the components (vertices, edges, diagonals and faces) of the cube, one of the Platonic solids.

Mathematics

Keywords

cube, vertex, edge, face, face diagonal, space diagonal, neighbouring faces, solid geometry, mathematics

Related items

### Cube

A cube is a rectangle that has edges of equal length. The cube is one of the five Platonic solids.

Properties

Number of vertices (V): 8

Number of edges (E): 12

Number of faces (F): 6

Euler´s formula is also valid for cubes:

F + V - E = 2

• A
• B
• C
• D
• E
• F
• G
• H

## Vertices

Cubes have 8 vertices. These are marked by capital letters of the alphabet. To each vertex belong 3 edges and 3 faces.

• vertex
• edge
• face

## Edges

Cubes have 12 edges, each marked with two capital letters. Eg.: AB, DH,…

Two faces meet along one edge. Any two edges meeting at one vertex are perpendicular to each other. For each edge there are 3 edges that are parallel to it. All edges have 4 skew edges, but all of them are perpendicular to it.

## Faces

Cubes have 6 faces. All of them are square and any two of them are congruent. They are marked with the letters of their vertices e.g. ABCD, CDHG,…

Faces are pairwise perpendicular to each other.

Each face has exactly one face parallel to it, while all other faces are perpendicular to it.

## Face diagonals

Cubes have 6 faces and each face has 2 face diagonals. Consequently, cubes have 12 face diagonals of equal length.

Choosing 3 faces sharing one common vertex and drawing their face diagonals, which do not pass through the chosen vertex, results in a regular triangle.

Similarly, 6 face diagonals form a tetrahedron in the cube.

The remaining face diagonals form a tetrahedron congruent with the previous one.

## Space diagonals

Cubes have 4 space diagonals passing through one common point, i.e. the centre point of the cube. Space diagonals have the same length.

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#### Grouping of solids 1

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This animation presents the formulas to calculate the perimeter and area of shapes as well as the surface area and volume of solids.

#### Platonic solids

This animation demonstrates the five regular three-dimensional (or Platonic) solids, the best known of which is the cube.

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