Baiocchi Figures for Polyhexes

A Baiocchi figure is a figure formed by joining copies of a polyform and having the maximal symmetry for the polyform's class. For polyhexes, that means the symmetry of a regular hexagon, or 6-way rotary with reflection. If a polyhex lacks apothegmic bilateral symmetry (see illustration at right), its Baiocchi figures must be Galvagni figures or contain Galvagni figures. Claudio Baiocchi proposed the idea in January 2008. Baiocchi figures first appeared in Erich Friedman's Math Magic for that month.

Here are minimal known Baiocchi figures for polyhexes of orders 1 through 6. Not all these solutions are uniquely minimal.

Monohex

Dihex

Trihexes

Tetrahexes

Pentahexes

Holeless Variants

The red figures were found by Mike Reid. See Polyhex Oddities.

Hexahexes

Heptahexes

For holeless variants, see Heptahex Oddities.

Last revised 2017-02-20.


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Col. George Sicherman [ HOME | MAIL ]