Convex Isoscelestriangle Polyhedra

The study of convex (no holes or notches) 3- dimensional polyhedra whose faces are isosceles triangles (two sides of one length, the third side of a different length) provides many new research problems suitable for high school and undergraduate students. These questions have their roots in mathematics whose investigation began over 2000 years ago! Before mentioning some specific research questions, let me put the questions in an historical context.