Galvagni Figures for Heptacubes

A heptacube is a solid made of seven cubes joined face to face.

A Galvagni figure is a figure that can be tiled by a polyform in more than one way—a kind of self-compatibility figure.

There are 607 heptacubes, or 1023 if we distinguish mirror images. This is too many to show here. Most require at most 4 tiles (with reflection), so they are fairly easy to find. Here are the Galvagni figures for heptacubes that require 6 or more tiles:

This heptacube has no Galvagni figure:

Last revised 2015-10-05.

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Col. George Sicherman [ HOME | MAIL ]