As A Graph
The skeleton of the dodecahedron—the vertices and edges—form a graph. The high degree of symmetry of the polygon is replicated in the properties of this graph, which is distance-transitive, distance-regular, and symmetric. The automorphism group has order 120. The vertices can be colored with 3 colors, as can the edges, and the diameter is 5.
The dodecahedral graph is Hamiltonian—there is a cycle containing all the vertices. Indeed, this name derives from a mathematical game invented in 1857 by William Rowan Hamilton, the icosian game. The game's object was to find a Hamiltonian cycle along the edges of a dodecahedron.
Read more about this topic: Dodecahedron
Famous quotes containing the word graph:
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)