(Grid = 12 x 12)
FOUR-POINTED STAR would seem to stray into a bit of crazy-quiltness — it's missing a few of its marbles. That's because the lighter halves of some of the star points have no color or delineation of their own, but instead merge into the background, whether that background is a solid or a print (see tiling pattern below).
The grid left illustrates the pattern as the block appears in THE COLLECTOR'S DICTIONARY OF QUILT NAMES AND PATTERNS (1980) by Yvonne M. Khin (p. 221), with no attempt to outline the missing pieces, though of course they have to be there. But the design stands out as more truly unique when the merged or hidden triangles are left hidden (see animation), especially since that's what makes the block so successful and so intriguing at first glance. The Ladies Art Company Catalogue published the pattern as EIGHT-POINTED STARS (#450), however, in an early 20th century addenda, but Khin's title is the more faithful.
Nevertheless, for such a mysterious quilt design, the title sounds rather pedestrian, a generic, nothing special, and anyway, if we're going to count points, why not call it an Eight-Pointed Star? Because it isn't an eight-point star, the four points each require three (visible) parts, in order to create all that magic of hide and seek. FOUR-POINTED STAR is a block designed like a written statement with an implication of much interest, but what is implied is never actually said. Great poetry derives from the same principle.
Compare at this site with DOVES IN THE WINDOW, and
TWENTY TEES, where the same sort of poetic sleight of hand is gloriously and vigorously at work.
FOUR-POINTED STAR is a Carrie Hall Block, illustrated in ROMANCE OF THE PATCHWORK QUILT IN AMERICA, published in 1935 (p.58-3) —
have a look at Hall's original at the Spencer Art Museum in Kansas.