matchstick question

[ccorn]

There are some slides by Erich Friedman on the topic. The slides also show the Harborth graph depicted in your copy of Number Freak. Using the string shown at the bottom of page 22 of Friedman's slides, you could elegantly build a 4-regular matchstick graph with 3*21 = 63 vertices and 126 edges. (page 28 contains it as a subgraph.) Yet Harborth's solution is the smallest known 4-regular matchstick graph with 52 vertices and 104 edges.