OFFSET
0,2
COMMENTS
There are many ways to tile the plane with the Goldberg tile; this is a particularly symmetric one.
In Cye Waldman's drawing, six copies of the gray sector are placed at the degree-4 vertices of the decagon, and 6 copies of a similar sector at the degree-6 vertices of the decagon.
REFERENCES
Goldberg, M. (1955). “Central Tessellations,” Scripta Mathematica, 21, pp. 253-260. See Fig.7b.
Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987; Fig. 1.3.6(a), page 30.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..2500
Rémy Sigrist, Illustration of initial terms
Rémy Sigrist, PARI program for A342285
N. J. A. Sloane, Illustration of initial terms (For example, the a(3) = 18 vertices at 3 steps from the center are colored blue; the a(4) = 30 vertices at 4 steps from the center are green with a black circle.)
Cye Waldman, The Goldberg Tile
Cye Waldman, Central portion of tiling.
Cye Waldman and others, Numerous postings to the Google Groups Tiling Mailing List about tilings with this Goldberg quadrilateral tile, March 2021.
FORMULA
Apparently, a(n) = 6*A138591(n-1) for n > 1. - Rémy Sigrist, Mar 30 2021
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 23 2021
EXTENSIONS
More terms from Rémy Sigrist, Mar 29 2021
STATUS
approved