There's nothing quite as good as mathematical toys for Christmas. After I had wrested this 'geomac' off the children, I made my very favourite shape - the stellated icosahedron.
I just love adding points to a platonic solid.
With 60 faces, 90 edges and 32 vertices, Euler's formula still holds true: 32+60-90=2 (vertices+faces-edges=2 for all solids without holes in them).
The question for young mathematicians is "do all the 3D shapes you know follow this rule?" and following on from this "can you make a 3D shape that doesn't follow this rule?" [clue: try making a donut out of geomac].