The Hirsch conjecture in dimension four

Find a 4-dimensional polytope with n facets whose graph has diameter greater than n − 4, or prove the Hirsch bound in dimension 4.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"discrete-geometry",
5	"combinatorics"
6	],
7	"type": "construction",
8	"also": [
9	"proof"
10	],
11	"source": {
12	"key": "frontiermath-open",
13	"name": "FrontierMath: Open Problems",
14	"url": "https://epoch.ai/frontiermath/open-problems/hirsch-conjecture",
15	"id": "hirsch-conjecture",
16	"curator": "Epoch AI",
17	"poser": "Warren M. Hirsch",
18	"status": "unsolved",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	},
22	"review": true,
23	"approval": "first-time"
24	}