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  "body": "\n## Definition\n\nLet $d \\ge 1$ and $m \\ge 1$, and let $a_1, b_1, \\dots, a_m, b_m$ be points of $\\R^d$.\nA *zonotope* is a set of the form\n$$Z = [a_1, b_1] + [a_2, b_2] + \\cdots + [a_m, b_m],$$\nthe [[Minkowski sum|7GK5417BJF]] of the [[line segments|VQ4Q2V45RP]] $[a_i, b_i]$.\n\n## Remarks\n\nEquivalently, $Z = \\set{c + \\lambda_1 v_1 + \\cdots + \\lambda_m v_m : 0 \\le \\lambda_i \\le 1}$ with $c = a_1 + \\cdots + a_m$ and $v_i = b_i - a_i$.\nSo $Z$ is the image of the cube $[0,1]^m$ under the affine map $\\lambda \\mapsto c + \\sum_i \\lambda_i v_i$, and $Z$ is a [[convex polytope|300K6CB1KH]].\nEvery zonotope is centrally symmetric about the point $c + \\tfrac12 (v_1 + \\cdots + v_m)$.\n\nExample: in $\\R^2$, take $v_1 = (1, 0)$, $v_2 = (\\tfrac12, \\tfrac{\\sqrt3}{2})$, $v_3 = (-\\tfrac12, \\tfrac{\\sqrt3}{2})$ and $c = 0$.\nThe sum of the three segments $[0, v_i]$ is a regular hexagon with side length $1$.\n\nNon-example: a triangle is not a zonotope, because it is not centrally symmetric.\n",
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