What is the relation between material.io and Polymer.js? Polymer along with database of paper components seem to already achieve all that material.io project provides (Material design based web components).
Polymer is a library that works towards enabling the use of the web platforms native features: shadowDom, templates, customElements (...and still HTMLImports) to create 'Web Components'. The Polymer Elements that ship with it are a collection of ready-made web components built with these guidelines. On top of this Polymer also adds some extra features such as data binding.
Material.io on the other side is a library that uses classic techniques such as CSS class scoping to build components for the web.
The relation between these both is not more than the style guide they use, Material Design.