Extra: regular polyhedra and cross-sections
Turn the regular polyhedrons, count their faces, vertices and edges and discover V − E + F = 2. Then cut a cube with a knife and see which shapes a cross-section can be.
- France: grade 9
- Germany: grade 8
- Iran: grade 7
- Syria: grade 8
- Ukraine: grade 11
- Russia: grade 10
Guide
This extra studio follows Iran's Year 7 enrichment book (chapter 6: cutting solids, the regular tetrahedron, building a regular dodecahedron) and the polyhedra lesson of its Year 9 enrichment book. It goes beyond the English curriculum.
A regular polyhedron has faces that are all the same regular polygon, with the same number meeting at every vertex. There are only five. V is the number of vertices, E of edges and F of faces.
In the cutting missions your child changes the knife's direction with the buttons and moves it with the slider. Common mistakes: thinking a cube can only be cut into squares, and counting every edge twice (once for each face).