Properties
- The dihedral angle of a dodecahedron is 2 arctan(φ) or approximately 116.5650512 degrees (where again φ = (1 + √5) / 2, the golden ratio). A137218
- If the original dodecahedron has edge length 1, its dual icosahedron has edge length φ.
- If the five Platonic solids are built with same volume, the dodecahedron has the shortest edges.
- It has 43,380 nets.
- The map-coloring number of a regular dodecahedron's faces is 4.
- The distance between the vertices on the same face not connected by an edge is φ times the edge length,
Read more about this topic: Dodecahedron
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)