It is an example of Platonic solids, described as cosmic stellation by Plato in his dialogues, and it was used as part of Solar System proposed by Johannes Kepler.

However, the regular dodecahedron, including the other Platonic solids, has already been described by other philosophers since antiquity.

The regular dodecahedron's metric properties and construction are associated with the golden ratio.

Its property of the Hamiltonian, a path visits all of its vertices exactly once, can be found in a toy called icosian game.

The regular dodecahedron is a polyhedron with twelve pentagonal faces, thirty edges, and twenty vertices.

Plato described the regular dodecahedron, obscurely remarked, "...the god used [it] for arranging the constellations on the whole heaven".

"[3] Aristotle also postulated that the heavens were made of a fifth element, which he called aithêr (aether in Latin, ether in American English).

[4] Following its attribution with nature by Plato, Johannes Kepler in his Harmonices Mundi sketched each of the Platonic solids, one of them is a regular dodecahedron.

[5] In his Mysterium Cosmographicum, Kepler also proposed the Solar System by using the Platonic solids setting into another one and separating them with six spheres resembling the six planets.

[6] Many antiquity philosophers described the regular dodecahedron, including the rest of the Platonic solids.

Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist.

Propositions 13–17 in Book XIII describe the construction of the tetrahedron, octahedron, cube, icosahedron, and dodecahedron in that order.

For each solid, Euclid finds the ratio of the diameter of the circumscribed sphere to the edge length.

Iamblichus states that Hippasus, a Pythagorean, perished in the sea, because he boasted that he first divulged "the sphere with the twelve pentagons".

In fact, each of the twelve vertices of the icosahedron divides an edge of the octahedron according to the "golden section".

(The reciprocal compound, of five cubes whose vertices belong to a dodecahedron, is a stellated triacontahedron.)

Further, we can choose one tetrahedron from each stella octangula, so as to derive a compound of five tetrahedra, which still has all the rotation symmetry of the icosahedron (i.e. the icosahedral group), although it has lost the reflections.

By reflecting this figure in any plane of symmetry of the icosahedron, we obtain the complementary set of five tetrahedra.

The following Cartesian coordinates define the twenty vertices of a regular dodecahedron centered at the origin and suitably scaled and oriented:[20]

In 20th-century art, dodecahedra appear in the work of M. C. Escher, such as his lithographs Reptiles (1943) and Gravitation (1952).

In Salvador Dalí's painting The Sacrament of the Last Supper (1955), the room is a hollow regular dodecahedron.

In modern role-playing games, the regular dodecahedron is often used as a twelve-sided die, one of the more common polyhedral dice.

The Megaminx twisty puzzle is shaped like a regular dodecahedron alongside its larger and smaller order analogues.

In the children's novel The Phantom Tollbooth, the regular dodecahedron appears as a character in the land of Mathematics.

Each face of the regular dodecahedron describes the various facial expressions, swiveling to the front as required to match his mood.

[citation needed] The fossil coccolithophore Braarudosphaera bigelowii (see figure), a unicellular coastal phytoplanktonic alga, has a calcium carbonate shell with a regular dodecahedral structure about 10 micrometers across.

Some regular crystals such as garnet and diamond are also said to exhibit "dodecahedral" habit, but this statement actually refers to the rhombic dodecahedron shape.

This was proposed by Jean-Pierre Luminet and colleagues in 2003,[29][30] and an optimal orientation on the sky for the model was estimated in 2008.

[36] Geometrically, this can be visualized as the ten-vertex equatorial belt of the dodecahedron connected to the two 5-vertex polar regions, one on each side.

The high degree of symmetry of the polygon is replicated in the properties of this graph, which are distance-transitive, distance-regular, and symmetric.