Polyhedra

Given \(n\) congruent squares, we can ask how many convex shapes can be formed. In this case the answer is easy, because the only convex shapes possible are rectangles. The number of rectangles can be found by taking the number of proper divisors of the number, dividing that by 2, then rounding that up to the nearest whole number. Here's the OEIS entry for the number of distinct convex shapes that can be formed with \(n\) congruent isosceles right triangles. Reflections are not counted as different. We could ask kids to find the number of convex shapes for some of the shapes that make up polyanimals. For example, given 10 congruent equilateral triangles, how many convex polygons can you make?