adobe illustrator - Filling areas using transparent color without affecting the border

I am drawing a figure which shows several tetrahedrons in Illustrator. I have drawn all the line segments and connected them at the endpoints. Now the figure has been like this.

Now I want to fill the areas surrounded by the line segments. I did this as follows: first selected 3 line segments, join them and fill the color.

However, I found another problem. Since there are dashed lines in this figure, if the 3 line segments contains one which is dashed, the join operation will cause all the lines dashed. That is what I don't want.

So What is the correct operation if I want to meet my purpose?