The first thought that strike me when I read your question was Picasso. I always had this feeling, that Picasso's art were both ugly and beautiful.
Some of the Pablo Picasso's art work which I consider as both ugly and beautiful are Woman with Mustard Pot (1910), Femme assise (1909), or Old Woman (1901) are few examples.
I suspect that there is any single bewildering antinomy term which describes the paradoxical idea of something being both ugly and beautiful at the same time.
But we can give a try!
Merriam Webster defines cosmeticize as:
to make (something unpleasant or ugly) superficially attractive
The other word is ugly-duckling. It doesn't precisely talk about being ugly and beautiful at the same time.
Merriam Webster defines ugly duckling
one that appears very unpromising but often has great potential
The other English phrase that we can use is 'aesthetically ugly'. It accommodates both ugly and beautiful at the same time.
You can also read newspaper article on Ugly is the new beautiful: From aesthetic monstrosity to design masterpiece. The second picture in this article is of toy troll.
Excerpt from the news article:
His book Ugly explores the complexities of ugliness and makes the point that without ugliness, there would be no beauty. He has cherry-picked items for his book, including kitsch flying ducks, hideous pink-haired troll dolls – even the postmodernist architecture of the Sainsbury Wing of the National Gallery gets singled out. Ugliness is fascinating, he claims – take the repugnant The Ugly Duchess by Quentin Massys – "It's one of the most popular postcards sold in London's National Gallery shop and rivals the sales of Monet's tranquil Water-Lilies," he says.
Secondly, if you want to describe something as beautiful and terrible at the same time then you can read this questions and my answer.
You can read more about golden ratio on wiki article. It certainly talks about aesthetics.