Even the size you use in your examples, https://abs.twimg.com/emoji/v1/36x36/2764.png, yields a broken image. However, https://abs.twimg.com/emoji/v1/72x72/2764.png works perfectly fine.
This is a documentation bug, you should not use those links but those provided by MaxCDN where both http://twemoji.maxcdn.com/16x16/2764.png and http://twemoji.maxcdn.com/36x36/2764.png are served just fine, together with http://twemoji.maxcdn.com/72x72/2764.png
Please update any code you have that points at abs.twimg since those links will be changed/updated without any notice.
I will update the documentation though, so thanks for the report.
I'm also having problem with flag emojis in sizes of 16x16 and 32x32.
/** Parse flag emojis for the country-list npm package */
const flag = twemoji.parse(countries[ISO].emoji, { size: '16x16'});
<!-- Resulting HTML -->
<img class="emoji" draggable="false" alt="🇷🇸" src="https://twemoji.maxcdn.com/v/12.1.5/16x16/1f1f7-1f1f8.png"/>
And a call to https://twemoji.maxcdn.com/v/12.1.5/16x16/1f1f7-1f1f8.png results in a 404. Is that expected?
Same issue as t1gor here.
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I'm also having problem with flag emojis in sizes of 16x16 and 32x32.
And a call to https://twemoji.maxcdn.com/v/12.1.5/16x16/1f1f7-1f1f8.png results in a 404. Is that expected?