Take each face of a cube and chop it into 8 triangles. If you pick any triangle, say the black one, there are symmetries of the cube that flip it over to the 3 neighboring ones. The first symmetry changes which vertex of the cube your triangle touches. The second changes which edge of the cube it touches. The third changes which face it lies on. Together, they generate the Coxeter group of the cube... which you'll understand if you click the link and read on!

#4d