Update cetz & ci
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.4.2"
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= Wallpaper Symmetries
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.4.2"
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= Mirror Symmetry
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.4.2"
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= Rotational Symmetry
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.4.2"
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#let pat(img, sol) = {
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problem()
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.4.2"
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= The Signature-Cost Theorem
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@ -7,23 +7,20 @@
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First, we'll associate a _cost_ to each type of symmetry in orbifold notation:
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#v(4mm)
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#align(
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center,
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table(
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stroke: (1pt, 1pt),
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align: center,
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columns: (auto, auto, auto, auto),
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[*Symbol*], [*Cost*], [*Symbol*], [*Cost*],
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[#sym.circle.small], [2], [#sym.times or #sym.convolve], [1],
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[#sym.diamond.stroked.small`2`], [1/2], [#sym.convolve`2`], [1/4],
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[#sym.diamond.stroked.small`3`], [2/3], [#sym.convolve`3`], [1/3],
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[#sym.dots], [#sym.dots], [#sym.dots], [#sym.dots],
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[#sym.diamond.stroked.small`n`],
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[$(n-1) / n$],
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[#sym.convolve`n`],
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[$(n-1) / (2n)$],
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),
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)
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#align(center, table(
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stroke: (1pt, 1pt),
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align: center,
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columns: (auto, auto, auto, auto),
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[*Symbol*], [*Cost*], [*Symbol*], [*Cost*],
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[#sym.circle.small], [2], [#sym.times or #sym.convolve], [1],
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[#sym.diamond.stroked.small`2`], [1/2], [#sym.convolve`2`], [1/4],
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[#sym.diamond.stroked.small`3`], [2/3], [#sym.convolve`3`], [1/3],
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[#sym.dots], [#sym.dots], [#sym.dots], [#sym.dots],
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[#sym.diamond.stroked.small`n`],
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[$(n-1) / n$],
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[#sym.convolve`n`],
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[$(n-1) / (2n)$],
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))
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We then calculate the total "cost" of a signature by adding up the costs of each component.
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