Given $t \in \mathbb{R}[0,1]$, consider the following set of polynomials:
$ \left[-{\left(t - 1\right)}^{2} t, {\left(t - 1\right)} {\left(t^{2} - t - 1\right)}, -{\left(t^{2} - t - 1\right)} t, {\left(t - 1\right)} t^{2}\right]. $
They show up as the coefficients of an interpolation filter. I've put them in a form that reminds me of Bernstein polynomials. They sum to unity, but don't appear to be orthogonal on $[0,1]$. They might be with respect to some weight function (or other interval).
Other than digging through lists of various types of polynomials, I'm at a loss for terminology to use in searching for further information. Does anyone recognize these as being part of some larger class, regardless of their connection to interpolation?