= Solution
A real spacetime point $p$ is represented by its <twistor line> $L_p\cong\mathbb{CP}^1$, lying entirely in <projective null twistor space>. Each point of $L_p$ is a <null twistor> specifying one real <null geodesic> through $p$. Their union is the null cone with vertex $p$. Thus the \b[twistor description of the null cone] is the family of null geodesics parametrized by the single line $L_p\subset PN$.
Equivalently, the spacetime points on that cone are precisely those whose <twistor lines> meet $L_p$:
$$
\boxed{\mathcal C_p=\{q\in M_{\mathbb R}:L_q\cap L_p\ne\varnothing\}.}
$$
For distinct finite points this follows immediately from the incidence equations: a shared nonzero $\pi$ obeys $(q-p)^{AA'}\pi_{A'}=0$, which is equivalent to $\det(q-p)=0$, the null-separation condition. The flag description extends it to the compact spacetime. Projective null twistors encode whole unoriented null geodesics, so this includes both future and past generators; a time orientation and an affine patch distinguish the two halves. The line itself is the sphere of null directions at the vertex, not a three-dimensional image of the cone embedded pointwise into twistor space.
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