Israeli society has experienced significant political polarization in recent years, reflected in five Knesset elections held within a four-year period (2019-2022). Public discourse increasingly references hypothetical divisions of the country into politically homogeneous "cantons." This paper develops a data-driven algorithmic approach to explore such divisions using publicly available municipality-level election results and geographic boundary data. We partition 255 Israeli municipalities, including the Israeli local authorities in Judea and Samaria, into cantons of neighbouring municipalities that maximize internal political similarity. We evaluate four clustering algorithms (Simulated Annealing, Agglomerative Clustering with contiguity constraints, Louvain Community Detection, and a K-Means baseline), four feature representations, three distance metrics and six values of K (3-20): 264 configurations. BlocShares with Agglomerative clustering gives the highest silhouette score (0.987 with Cosine distance), while NMF with Louvain community detection best balances political homogeneity, silhouette quality (0.142) and interpretability, with stable boundaries across the five elections (ARI 0.927). The resulting K=5 partition identifies five politically coherent regions -- a mixed center-right metropolitan core around Tel Aviv, a right-wing region from Jerusalem through the south and the Judea and Samaria authorities, a right-leaning northern region, an Arab canton, and a canton of the seven predominantly Haredi cities, held together by political similarity rather than shared borders. Built from the 2019-2021 elections only, the cantons still differ significantly in every bloc's vote share in the held-out 2022 election. An interactive web application accompanies this work.

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