Squares and cubes

In geometry, a cube^[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). It is special by being a cuboid and a rhombohedron.



SNAP CUBES

I remmebered these cube blocks we used to use in maths in school and thought these could be a visual to look at. As an actual object they are probably too childish to use and will most likely remind people school but if they were used in the right context and made up an image or FILM FESTIVAL they may work.

The cube has three uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123.
The cube has three classes of symmetry, which can be represented by vertex-transitive coloring the faces. The highest octahedral symmetry O_h has all the faces the same color. The dihedral symmetry D_4h comes from the cube being a prism, with all four sides being the same color. The lowest symmetry D_2h is also a prismatic symmetry, with sides alternating colors, so there are three colors, paired by opposite sides.

A cube has eleven nets (one shown above): that is, there are eleven ways to flatten a hollow cube by cutting seven edges.^[2] To color the cube so that no two adjacent faces have the same color, one would need at least three colors.