The ancient Greeks discovered five types of 3-dimensional solids with very nice symmetries, and came up with various reasons why they should care about them. For example, Plato conjectured that the icosahedron is the shape of all water particles. Unfortunately, the ancient Greeks did not discover p-adic numbers. In this talk I will attempt to explain: what is a p-adic icosahedron and why should we care about it? Speaker(s): Harry Richman (UM)