Symbol for the starts of 18-, 27-, 46- and 58-Across

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XXX.

Last seen on: NY Times Crossword 30 Dec 21, Thursday

Random information on the term “XXX”:

30 (thirty) is the natural number following 29 and preceding 31.

Thirty is the sum of the first four squares, which makes it a square pyramidal number.

It is a primorial.

It is a pronic number.

30 is the smallest sphenic number, and the smallest of the form 2 × 3 × r, where r is a prime greater than 3. 30 has an aliquot sum of 42; the second sphenic number and all sphenic numbers of this form have an aliquot sum 12 greater than themselves.

Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number.

30 is the largest number such that all coprimes smaller than itself, except for 1, are prime.

A polygon with thirty sides is called a triacontagon.

The icosahedron and the dodecahedron are Platonic solids with 30 edges. The icosidodecahedron is an Archimedean solid with 30 vertices, and the Tutte–Coxeter graph is a symmetric graph with 30 vertices.

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