Yes.  In a perfect dodecahedron, all elements are exactly equal.  For fun, I
did a trigonometric analysis of the dodecahedron when I was very interested in
domes.  There are lots of nice, pretty relationships in there that you can find
with a little patience and a calculator.
    For starters, imagine a regular pentagon using unit length edges.  Now
calculate the length of the diagonal.  From there, you should be able to get a
grasp on the corner of your dodecahedron, and you can do it with simple trig.
Here is a helpful clue.  You may know that the icosahedron is the "inverse" of
the dodecahedron.
    Play with the numbers and soon you will find the face angle, the distance to
center, and all the needed relationships to calculate anything about it.  You
can work it all out with little more than Pythagoras' Theorem if you are
patient.

Cheers!

Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip

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