  Let $P$ be a polynomial of degree $d$ with a Cremer point $p$ and no
repelling or parabolic periodic bi-accessible points. We show that there are
two types of such Julia sets $J_P$. The \emph{red dwarf} $J_P$ are nowhere
connected im kleinen and such that the intersection of all impressions of
external angles is a continuum containing $p$ and the orbits of all critical
images. The \emph{solar} $J_P$ are such that every angle with dense orbit has a
degenerate impression disjoint from other impressions and $J_P$ is connected im
kleinen at its landing point. We study bi-accessible points and locally
connected models of $J_P$ and show that such sets $J_P$ appear through
polynomial-like maps for generic polynomials with Cremer points.
