Tell me about my Icosahedron (and win an art print)

This is for an art project of mine involving modelling gothic steampunk spores for Made In Newcastle.

The first to provide the answers to these questions will be the recipient of a print of one of the final images, printed by Bondgate Galleries. Which will be very nice, and probably about 12” square. This is a very early test render, the final product will be much more awesome.

Very early test sketch of the kind of prints i'll be creating.

So then... in an Icosahedron as described in the diagram below,  O is the centre point of the whole shape, D is the north pole. (Obviously i'm looking for angles on an actual Icosahedron, not the angles on the picture)

Now the answer to Q1 may well be 60° and the answers to Q2 may be 90°, but I'm thinking not... Even if so, confirmation is valuable to me.

Q1) What is the angle DOB?

Q2) If we call the mid point of the triangle CBK X, and the mid point of the triangle CLK Y, and assume that they’re not at 90°...

A)  What is the angle DOX?
B)  What is the angle DOY?

Q3) If we call the midpoint of the triangle DCB Z, What is the angle DOZ?

(if you know this stuff, please post some kind of explanation not just numbers though!)