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Regular dodecahedron

A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, and 160 diagonals (60 face diagonals, 100 space diagonals).[2] It is represented by the Schläfli symbol {5,3}.

The of a regular dodecahedron is 2 arctan(ϕ) or approximately 116.565° (where again ϕ = 1 + √5/2, the golden ratio). OEIS: A137218 Note that the tangent of the dihedral angle is exactly −2.

dihedral angle

If the original regular dodecahedron has edge length 1, its dual has edge length ϕ.

icosahedron

If the five Platonic solids are built with same volume, the regular dodecahedron has the shortest edges. It is the roundest of the five Platonic solids, enclosing the most volume within the same radius.

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, because the diagonal of a pentagon is ϕ times its edge length.

If two edges share a common vertex, then the midpoints of those edges form a 36-72-72 with the body center.

golden triangle

Regular dodecahedron graph

20

30

5

5

5

120 (A5 × Z2)[20]

3

Hamiltonian, regular, symmetric, distance-regular, distance-transitive, 3-vertex-connected, planar graph

a regular polychoron (4D polytope whose surface consists of 120 dodecahedral cells)

120-cell

− A dodecahedron shaped coccolithophore (a unicellular phytoplankton algae).

Braarudosphaera bigelowii

(molecule)

Dodecahedrane

Pentakis dodecahedron

Snub dodecahedron

Truncated dodecahedron

"Regular Dodecahedron". MathWorld.

Weisstein, Eric W.

Klitzing, Richard. .

"3D convex uniform polyhedra o3o5x – doe"

Editable printable net of a dodecahedron with interactive 3D view

The Uniform Polyhedra

– Models made with Modular Origami

Origami Polyhedra

– 3-d model that works in your browser

Dodecahedron

Virtual Reality Polyhedra

VRML

K.J.M. MacLean, A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra

Dodecahedron 3D Visualization

: Software used to create some of the images on this page.

Stella: Polyhedron Navigator

How to make a dodecahedron from a Styrofoam cube

The Greek, Indian, and Chinese Elements – Seven Element Theory