Galvagni Figures for Polyaboloes

A polyabolo is a planefigure formed by joining equal isosceles right triangles along equal edges. A Galvagni figure is a figure that can be tiled by a polyform in more than one way—a kind of self-compatibility figure. Galvagni figures first appeared in Erich Friedman's Math Magic for November 2004.

Here are minimal known Galvagni figures for polyaboloes. Some polyaboloes have solutions that are technically Galvagni figures but are not polyaboloes. They are formed by joining parallelograms to make voided rhombuses.

Monabolo

Diaboloes

Impossible

Non-polyabolo Solution

Triaboloes

Mirror-Symmetry Variant

Holeless

Impossible

Non-polyabolo Solution

Tetraboloes

Holeless Variant

Impossible

Non-polyabolo Solutions

Pentaboloes

Holeless Variants

Mirror-Symmetric Variants

Impossible

Non-polyabolo Solution

Hexaboloes

Mirror-Symmetric Variants

Unsolved or Impossible

Non-polyabolo Solutions

Last revised 2014-10-28.


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Col. George Sicherman [ HOME | MAIL ]