Hatcher 0.22

Hatcher, Algebraic Topology, Chapter 0

22. Let $X$ be a finite graph lying in a half-plane $P\subset\mathbb{R}^3$ and intersecting the edge of $P$ in a subset of the vertices of $X$. Describe the homotopy type of the `surface of revolution’ obtained by rotating $X$ around the edge of $P$.

Proof. Consider the image shown in the document here.

$\square$