Question

How many edges does a cube have?

Answer 1

`12`

Explanation:

A cube, otherwise known as a regular hexahedron has `6` square faces.

Each face has `4` edges, but every edge is shared between `2` faces.

So there are a total of `(6 xx 4) / 2 = 12` edges.

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Bonus

In three dimensions there are `5` regular polyhedra, namely:

• Tetrahedron
• Cube (regular hexahedron)
• Octahedron
• Dodecahedron
• Icosahedron

In four dimensions there are `6` regular polytopes, namely:

• Pentachoron
• Tesseract (regular octachoron)
• Regular hexadecachoron.(16-cell)
• Icositetrachoron (24-cell)
• Hecatonicosachoron (120-cell)
• Hexacosichoron (600-cell)

In five dimensions and above there are just `3` regular polytopes:

• Regular simplex (analogue of the tetrahedron)
• Regular measure polytope (analogue of the cube)
• Regular cross polytope (analogue of the octahedron)

The `n`-dimensional analogue of the cube has `2^n` vertices and `2n` facets of dimension `n-1`. Each of the `2^n` vertices has `n` adjacent vertices, resulting in a total of `n*2^(n-1)` edges.