The rhombic dodecahedron may also appear in the garnet crystal, the architectural philosophies, practical usages, and toys.

The rhombic dodecahedron is a polyhedron with twelve rhombi, each of which long face-diagonal length is exactly

[2] It is face-transitive, meaning the symmetry group of the solid acts transitively on its set of faces.

The rhombic dodecahedron can be viewed as the convex hull of the union of the vertices of a cube and an octahedron where the edges intersect perpendicularly.

For edge length √3, the eight vertices where three faces meet at their obtuse angles have Cartesian coordinates (±1, ±1, ±1).

The rhombic dodecahedron can be seen as a degenerate limiting case of a pyritohedron, with permutation of coordinates (±1, ±1, ±1) and (0, 1 + h, 1 − h2) with parameter h = 1.

Therefore, the rhombic dodecahedron has twice the volume of the inscribed cube with edges equal to the short diagonals of the rhombi.

[5] Alternatively, the rhombic dodecahedron can be constructed by inverting six square pyramids until their apices meet at the cube's center.

It is dual to the tetroctahedrille or half cubic honeycomb, and it is described by two Coxeter diagrams: and .

As Johannes Kepler noted in his 1611 book on snowflakes (Strena seu de Nive Sexangula), honey bees use the geometry of rhombic dodecahedra to form honeycombs from a tessellation of cells each of which is a hexagonal prism capped with half a rhombic dodecahedron.

In these cases, four vertices (alternate threefold ones) are absent, but the chemical bonds lie on the remaining edges.

[9] A rhombic dodecahedron can be dissected into four congruent, obtuse trigonal trapezohedra around its center.

Spacecraft mass properties influence overall system momentum and agility, so decreased variance in envelope boundary does not necessarily lead to increased uniformity in preferred axis biases (that is, even with a perfectly distributed performance limit within the actuator subsystem, preferred rotation axes are not necessarily arbitrary at the system level).

The collections of the Louvre include a die in the shape of a rhombic dodecahedron dating from Ptolemaic Egypt.

The faces are inscribed with Greek letters representing the numbers 1 through 12: Α Β Γ Δ Ε Ϛ Z Η Θ Ι ΙΑ ΙΒ.

[15] It is isohedral with tetrahedral symmetry order 24, distorting rhombic faces into kites (deltoids).

Like many convex polyhedra, the rhombic dodecahedron can be stellated by extending the faces or edges until they meet to form a new polyhedron.

The rhombic dodecahedron forms the hull of the vertex-first projection of a tesseract to three dimensions.

The rhombic dodecahedron can be decomposed into six congruent (but non-regular) square dipyramids meeting at a single vertex in the center; these form the images of six pairs of the 24-cell's octahedral cells.

The non-regularity of these images are due to projective distortion; the facets of the 24-cell are regular octahedra in 4-space.

The triangular faces of each pair of adjacent pyramids lie on the same plane, and so merge into rhombi.