Definition

A cube has $6$ faces, $12$ edges and $8$ vertices

Mensuration • Solids • Cube

Statement

A cube (and equally a cuboid) is bounded by

6

rectangular faces meeting in

12

edges at

8

vertices; each edge is shared by exactly two faces and each vertex by exactly three, so counting

4

edges on each of the

6

faces gives

24

edge-instances and the true edge count is

24 \div 2 = 12

How to use it

1Count the edges in three groups of four — the top square, the bottom square, and the four verticals joining them.
2Whenever a per-face count is used, divide by $2$ for edges and by $3$ for vertices, because faces share them.
3Use it for any 'one strip, one rod or one bead per edge' assembly question: the number of pieces is $12$ , not $6$ and not $24$ .
4Euler's relation $F - E + V = 2$ checks the three counts against each other: $6 - 12 + 8 = 2$ .

A wire frame in the shape of a cube of edge

5

cm is to be made. What total length of wire is needed?

Step-by-step

1
Number of edges $= 12$
Why: Four on the top face, four on the bottom, four vertical.
2
Total length $= 12 \times 5 = 60$ cm

Answer

60

Watch out

The

6

in 'six faces' is the count a question about surface area wants, not the count a question about joins, rods or edges wants; using

6

or the uncorrected

24

in place of

12

is the standard error here.

Also known as

edges of a cube, faces edges vertices, how many edges has a cube, cube edge count, Euler formula for polyhedra