
 Dodecahedron 
 Vertex description: 5.5.5
 Faces: 12
 Edges: 30
 Vertices: 20
 Dual: Icosahedron
 Stellations:
 Fully supported: 4 (4 reflexible, 0 chiral)
 Miller's rules: 4 (4 reflexible, 0 chiral)
One of the five regular convex polyhedra known as the Platonic solids.
This model was made from a single connected net, printed on one sheet of A4
paper. Nets can be generated and printed at any size using any of
Small Stella,
Great Stella,
or
Stella4D,
even in the free demo versions.
Above is a dodecahedron with photos of a cat on each face (seen from
above, below, and in original net form).
Stella
allows you to map photos onto faces in 3D. The images then appear on nets when
you print them out, ready to be cut out, folded up, and glued together as seen
here.
Here's another model. This time the photos were fitted inside each face,
rather than around each face, so a border is visible.

Here's a dodecahedron in Stella, using a 3view layout featuring the
dodecahedron itself, the unfolded net, and a partially folded net.
See more screenshots here.


Here is a compound of the
dodecahedron with its dual.
Notice how the dodecahedron's vertices sit above the icosahedron's
faces, and vice versa? Also the edges of the two polyhedra bisect each
other at rightangles.


Multiple dodecahedra can be arranged in an intersecting manner to form
various compounds.
Here is one consisting of 5 intersecting dodecahedra.


The dodecahedron has three
stellations. Here is the
first, the small stellated dodecahedron. It's also a faceting of the
icosahedron.


Second stellation, the great dodecahedron. This one is also a faceting
of the icosahedron.


Third and final stellation, the great stellated dodecahedron.
This is also an example of a
faceting of the
dodecahedron. The dodecahedron has quite a few facetings.
You should be able to see that this polyhedron's vertices are the same
as that of a dodecahedron (this is all faceting means).


Some of its facetings are compounds of other Platonic solids, such as
this compound of 5 cubes.


The compound of 5 tetrahedra is another wellknown faceting.


The compound of 10 tetrahedra is yet another wellknown faceting.


Subsymmetric stellations are also possible. These are stellations that
have less symmetry than the dodecahedron itself. The polyhedron shown
here is an example. It's hard to tell looking at it, but this
polyhedron's faces lie in the same planes as the faces of a regular
dodecahedron (this is what makes it a stellation).


Another subsymmetric stellations of the dodecahedron. This one
highlights the relationship between the three fully symmetric
stellations, with the spikes of the final
stellation (great stellated dodecahedron) visible outermost, but
with some missing to reveal the inner stellation layers, and the
small stellated dodecahedron showing
inside.

