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As discussed in Why lord Shiva has a crescent moon on his head? and Why is Moon on Lord Shiva's head only shown as crescent?, we know that a crescent is always shown on head of Shiva. It's not a full moon or half.

So what phase of moon is usually represented on Shiva's head? Thank you.

sbharti
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It would be the 12th day waning crescent moon.

From the links shared in the question body it is clear that moon came to reside on Shiva's head to cool down the effect from Kālakūṭa poison that he had devoured. This happened on Ekadashi, and next day moon came out

From Chp 10 of Brahma Kanda, Padma Purana

Then on the twelfth day in the morning, when the sun had risen, the great Lakṣmī, graced with all (auspicious) characteristics, sprang up. All the religious deities saw that great mother of all creatures having her abode in the heart of Viṣṇu, and were delighted. Then, the cool-rayed one (i.e. the Moon), the brother of Lakṣmī, sprang up with nectar. (So also) Tulasī, Viṣṇu’s wife, purifying the world, came up.

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    But as seen from India, which is entirely in the northern hemisphere, the crescent moon shown in the two linked items would be waxing, not waning. – Ray Butterworth Oct 26 '21 at 13:03
  • @RayButterworth Mahashivaratri although happens on Krishna Trayodashi – sbharti Oct 26 '21 at 22:13
  • @Ray Butterworth It is my understanding that waning is the phase where the moon goes from full moon to new moon. On the 12th day the visible area is what we see in imagery of Lord Shiva – Artist Formerly Known As CSD Oct 28 '21 at 16:34
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    @Carmensandiego, Waxing Crescent Moon is what a waxing crescent looks like from Texas, which is a similar latitude to India, and which looks just like the moon in the images linked from the question. A waning crescent moon would look like that only from the southern hemisphere (e.g. Australia). ¶ Assuming you live in the north, watch the sky over the next week. You'll see the moon waxing from half to crescent, in exactly the opposite orientation as the Shiva images. – Ray Butterworth Oct 28 '21 at 17:42
  • @RayButterworth - I don't see what role latitude plays here. Also as far as I know dictionary defines waning as something that progressively decreases. Also there are blog sites that have 12th day waning moon image in sync with the answer – Artist Formerly Known As CSD Nov 22 '21 at 10:35
  • @Carmensandiego, People in the northern and southern hemispheres each think the other is standing upside down. The view of the moon is upside down with respect to the other's view. In the north, the moon starts as a crescent like a letter "D", waxes to a full moon, and then wanes to a crescent like a letter "C". But in the south, it goes from "C" to "D" instead. The question's images show a "D", which in India is a waxing crescent. See: How the Moon’s phases look from the Earth — Open University. – Ray Butterworth Nov 22 '21 at 14:03
  • @RayButterworth - Thanks . Will read up more on how view is different in Northern and Southern hemisphere. On the the image itself there is not much to read on whether it is "C" or "inverse C". A quick Google search will reveal imagery with "C". See https://www.google.com/search?q=shiva+moon+over+head&oq=shiva+moon+over+head&aqs=chrome..69i57j0i22i30j0i390l4.4562j0j9&client=ms-android-samsung-gs-rev1&sourceid=chrome-mobile&ie=UTF-8 – Artist Formerly Known As CSD Nov 22 '21 at 14:17