The reason I got Stella, was to help me make stuff like this.
That's a dual of a 3V icosohedronal Geodesic dome, with a radius of 120 cm.
I'm working my way up to larger structures, the one I'm making now is a 5v dual. There's so much less cutting and joining with hexes than with triangles, I'm amazed that it's not standard practice for dome house construction!
You can then also use "Color->Basic Color Scheme->Same Color for Chiral Face Pairs" to reduce the number of colours from 4 to 2. Now mirrored faces share the same colour and you can see clearly the two truly different face types. Hopefully with this colouring it becomes clearer that the two face types fit into the model differently.