Overview
This article introduces an example of representing IIIF polygon annotations in TEI/XML.
Method
In TEI/XML, you can represent polygon annotations using the zone tag and the points attribute.
https://www.tei-c.org/release/doc/tei-p5-doc/en/html/ref-teidata.point.html
Example
For verification purposes, I added a TEI/XML export feature to the annotation tool introduced in the following article.
Specifically, the following download option was added.

An example of the TEI/XML obtained as a download result is shown below. Rectangles are described using ulx, uly, lrx, lry, while polygon information is described using points.
<?xml version="1.0" encoding="utf-8"?>
<?xml-model href="http://www.tei-c.org/release/xml/tei/custom/schema/relaxng/tei_all.rng" type="application/xml" schematypens="http://relaxng.org/ns/structure/1.0"?>
<?xml-model href="http://www.tei-c.org/release/xml/tei/custom/schema/relaxng/tei_all.rng" type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0">
<teiHeader>
<fileDesc>
<titleStmt>
<title>
Title
</title>
</titleStmt>
<publicationStmt>
<p>
Publication Information
</p>
</publicationStmt>
<sourceDesc>
<p>
Information about the source
</p>
</sourceDesc>
</fileDesc>
</teiHeader>
<text>
<body>
<p>
Some text here.
</p>
</body>
</text>
<facsimile sameAs="https://dl.ndl.go.jp/api/iiif/3437686/manifest.json">
<surface sameAs="https://dl.ndl.go.jp/api/iiif/3437686/canvas/1">
<graphic url="https://dl.ndl.go.jp/api/iiif/3437686/R0000001/full/full/0/default.jpg" sameAs="https://dl.ndl.go.jp/api/iiif/3437686/R0000001"/>
<zone ulx="5314" uly="1983" lrx="5509" lry="2189" ana="Cを変更" points="5314,2087 5412,1984 5510,2087 5412,2190 5314,2087 5314,2087"/>
<zone ulx="478" uly="307" lrx="1226" lry="3731" ana="校異源氏物語" points="478,3732 478,308 1227,308 1227,3732 478,3732"/>
</surface>
<surface sameAs="https://dl.ndl.go.jp/api/iiif/3437686/canvas/3">
<graphic url="https://dl.ndl.go.jp/api/iiif/3437686/R0000003/full/full/0/default.jpg" sameAs="https://dl.ndl.go.jp/api/iiif/3437686/R0000003"/>
<zone ulx="2197" uly="3044" lrx="2731" lry="3573" ana="サンプル" points="2209,3045 2198,3551 2729,3575 2732,3062 2209,3045"/>
<zone ulx="993" uly="3701" lrx="2849" lry="4095" ana="中央公論社蔵版" points="993,4096 993,3702 2849,3702 2849,4096 993,4096"/>
</surface>
</facsimile>
</TEI>
Below is an example displayed in Oxygen XML Editor.

Below is a display example of the IIIF annotation, showing that the same rectangles can be represented.

Summary
I hope this serves as a useful reference for integrating IIIF and TEI.