Cube have octahedral symmetry. The cube is a part of a sequence of rhombic polyhedra and tilings with ["n",3] Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are squares. The cube is a square prism: As a trigonal trapezohedron, the cube is related to the hexagonal dihedral symmetry family. It is an element of 9 of 28 convex uniform honeycombs: It is also an element of five four-dimensional uniform polychora: The skeleton of the cube (the vertices and edges) form a graph, with 8 vertices, and 12 edges. It is a special case of
Prince Rupert's cube be passed through a hole made in another cube "of the same size" without splitting the cube into two pieces. If two points are placed on two adjacent edges of a unit cube, each at a distance of 3/4 from the point where the two edges meet, then the distance between the two points will be These two points, together with a second set of two points placed symmetrically on the opposite face of the cube, form the four vertices of a square that lies entirely within the unit cube. This square, extruded in both directions perpendicularly to itself, forms