Dear Julia and Liam,

Thanks for the typo alert. It is now corrected and noted on the Corrections page.

Regarding your polyhedra question, the point is that the icosidodecahedron can be constructed by lopping off the corners of the dodecahedron. Since this can't easily be done physically, the student does it graphically. It's interesting that the surface area doesn't change much, only about 7%.

Joan Cotter

Joan,

Liam understands your explanation and he says he 'gets it' now. Now that you have pointed it out, he sees that when you cut the corners off of the dodecahedron to make an icosadodecahedron, it creates triangles AND THE SMALLER PENTAGONS and that's why you wanted him to make the comparison and see the 7% difference in surface area.

I discussed this with him further to try to understand what he was thinking as he worked on this lesson. Throughout these lessons, he has built a dodecahedron, a truncated dodecahedron, and an icosadodecahedron.

At the time of this lesson, he only thought of the truncated dodecahedron as a dodecahedron with its corners lopped off. In fact, you lop off only a tiny bit of the corners to make large decagons and tiny triangles. However, to make an icosadodecahedron you lop off a larger piece of the corners to make bigger triangles than in the truncated dodecahedron and smaller pentagons than in the dodecahedron.

Since he built the models with the same size pentagons, he didn't readily see the connection between the pentagons in the icosadodecahedron and dodecahedron that you were pointing out in this lesson. But he can now see that the icosadodecahedron model he built would have come from an even larger dodecahedron.

Thanks again for your clarification.

Julia & Liam