Minimal Finite Model of Wedge Sum of Spheres

We classify minimal finite models of the Möbius band and several wedge sums of spheres. In particular, we show that the minimal finite model of the Möbius band coincides with that of the circle $S^1$. Furthermore, we prove that both $S^2\vee S^1$ and $S^2\vee S^2$ admit minimal finite models on exactly seven points, and that each of $S^1\vee S^1\vee S^2$, $S^1\vee S^1\vee S^1\vee S^2$, $S^1\vee S^2\vee S^2$, $S^2\vee S^2\vee S^2$, and $S^2\vee S^2\vee S^2\vee S^2$ admits a minimal finite model on exactly eight points.