I'm a "quick fix" / concept guy, so I'll see if I can do a quick and dirty on this.

Basic geometry:

Triangle - Three sides

Pentagon - Five sides (all same length)

Hexagon - Six sides (all same length)

Equilateral Triangle - all three sides are the same length and all three angles are 60 degrees each. (totaling 180 degrees)

Basic Dome stuff:

1V or frequency 1 dome is made of 15 equilateral triangles:

2V or frequency 2 dome is made of 30 triangles that form tented pentagons and 10 equilateral triangles:

3V or frequency 3 dome is roughly 1/2 of a "soccerball" pattern, with 30 triangles forming tented pentagons (black on a soccerball) and either 45 triangles or 75 triangles that form tented hexagons (white on a soccerball):

The reason for the different numbers for the 3V dome is because a soccerball shape does not cut evenly in half along the triangular sides, so you divide slightly more "3/8" or slightly less "5/8" than half a sphere.

Some basic math for a 3V dome:

E (edges) = pick a number. Say 3 feet

P (pentagon) = E times .08696 or 3 x .08696 = 2.6088 This makes the sides of the triangle shorter

H (hexagon) = E times 1.0224 or 3 x 1.0224 = 3.0672 This makes the sides of the triangle longer

The base of your dome will have 15 sides. And in this case will be approximately 7.5 feet tall and around 14 feet across.

You don't have to use triangles, but it rounds out your dome the higher frequency you have. You can have a 3V "flat sided" dome, using only flat hexagons and pentagons or a flat 2V if you use flat pentagons and equilateral triangles. It can be up to you. There are MANY possiblilites; just do what I did and Google images for geodesic domes and click pics and follow the links! You can also mine Youtube as I did for more information.

I could write an entire book on just the stuff I know, which barely scratches the surface of this. It's as simple or as complicated as you're willing to go with it. I say start small, make lots of models, measure carefully, have fun, don't quit and have an open mind.

If you want an easy project to get the feel of how to make a 1V model, get some heavy paper, some tape, a ruler, a compass and/or protractor and some scissors.

Make 15 equalatteral triangles and tape 10 together in a row. Connect the two ends to make a ring. Connect the other 5 to make a tented pentagon (tentagon?). Place the "tentagon" on top of your ring and tape the edges.

Congratulations! You've got a mini-dome!