"showed its face" is correct and widely used in written English.
It is usually used as an idiom meaning to become visible or appear. For example, "After days of cloudy skies, the sun finally showed its face."
We spent the next eight years giving the truth such a furious beating every time it showed its face that it eventually just stopped coming around altogether.
"And so on election night it showed its face, for maybe, probably, one of the first times in my adult life," he said.
Mr Swan forecast that it would be three more years before a surplus showed its face.
In 1315 and 1316, the sun barely showed its face.
A few days before the elections, Yiorgos Palis, a candidate then with Syriza in Lesbos and now MP for the island, told me that "the far-right showed its face here, but the people kept their cool".
In fact, the only visible evidence that a Very Important Foreigner was in town came from the Lebanese army which, for the first time since this war began, showed its face on the streets of Beirut in significant numbers, with soldiers standing nonchalantly in ones and twos on corners.
"And, when we least expect it, it shows its face and intimidates us.
If my light was true, then I needed it to show its face here, where it counts.
And young visitors should come away knowing that whether or not it shows its face, the Sun is undeniably a star.
Maybe it shows its face in r/TrueReddit, or in the New Yorker's Sunday newsletter, or in the Spotlight or Archive sections of newyorker.com.
But when the sun does have the decency to show its face it makes a glorious addition to Garsington's excellent Eugene Onegin – easily the best since Graham Vick's gold-standard 1994 production for Glyndebourne.
