Volume XXX

VOL XXX

Geombinatorics Quarterly

Issue 1 (July 2020)

A small 6-chromatic unit-distance graph in R3 By Aubrey de Grey 5
Polyiamonds Attaining Extremal Topological
Properties, Part I
By Greg Malen and Érika Roldán 14
What percent of the plane can be properly 5- and
6-colored?
By Jaan Parts 25
Moral Principles for My Young Colleagues, or
A Tale of Big Man and Little Bird
By Alexander Soifer    40

Issue 2 (October 2020)

Remembering John Horton Conway By Alexander Soifer 53
Remembering Ronald Lewis Graham By Alexander Soifer 56
Polyiamonds Attaining Extremal Topological Properties, Part II By Greg Malen and Érika Roldán 63
The chromatic number of the plane is at least 5
a human-verifiable proof
By Jaan Parts 77

Issue 3 (Jan 2021)

Why 7 ± 2? A Possible Geometric Explanation by Laxman Bokati, Vladik Kreinovich,
and Jordan Katz
109
On the Hollow Enclosed by Convex Sets by Jenő Lehel and Géza Tóth 113
Cops and Robbers on Toroidal Chess Graphs by Neil R. Nicholson and Allyson Hahn 123
The surface of a sufficiently large sphere
has chromatic number at most 7
 by Tomas Sirgedas 138
We have nothing to lose except everything by Alexander Soifer 152

Issue 4 (April 2021)

The Structure of the Heawood Graph by Emille Davie Lawrence and Robin T. Wilson 169

On upper bounds for the multi-fold chromatic numbers of the plane

by Jaan Parts 177

On the chromatic number of circular disks and infinite strips in the plan

by D.H.J. Polymath 190
Tilings with the Minimal Tile Propert  by Iwan Praton 202

Geometric Explanation for an Empirical Formula Describing Our Galaxy’s Warping

by  Julio Urenda,
Olga Kosheleva, and
Vladik Kreinovich
208