How to force GitHub Pages build?

Question

Every GitHub repository can have (or be) a GitHub Pages website, that can be built with Jekyll. GitHub builds the site every time you push a new commit.
Is there a way t

Answer 1

This is doable as of v3 of the GitHub API, though it is currently in preview https://developer.github.com/v3/repos/pages/#request-a-page-build

POST /repos/:owner/:repo/pages/builds