Polyform Oddities

    That is another of your odd notions, said the Prefect, who had the fashion of calling everything odd that was beyond his comprehension, and thus lived amid an absolute legion of oddities.
—Poe, The Purloined Letter

A polyform oddity is a geometric figure with binary symmetry or better, formed by joining an odd number of congruent polyforms. Oddities are also known as Sillke figures, after Torsten Sillke, who first studied them systematically.

This page shows minimal known oddities and similar constructions for various polyforms with various symmetries.


Polyomino Oddities. Oddities for polyominoes of order up to 7.
Pentomino Oddities. Pentomino oddities with specific symmetries.
One-Sided Pentomino Oddities. One-sided pentomino oddities with specific symmetries.
Hexomino Oddities. Hexomino oddities with specific symmetries.
Polyomino Semi-Oddities. Semi-oddities for polyominoes. A semi-oddity is a figure with quaternary symmetry and an even number of tiles that is not a multiple of 4.
Heptomino Oddities. Heptomino oddities with specific symmetries.


Triking Oddities. Oddities with specific symmetries for pseudopolyominoes of order 3.
Pentaking Oddities. Oddities with specific symmetries for pseudopolyominoes of order 5.


Pentiamond, Heptiamond, and Enneiamond Oddities. Oddities for pentiamonds, heptiamonds, and enneiamonds. Oddities for polyiamonds of odd order can have only bilateral symmetry.
Hexiamond Oddities. Hexiamond oddities with specific symmetries.
Octiamond Oddities. Octiamond oddities with specific symmetries.
Polyiamond Tri-Oddities. These are like oddities but with ternary symmetry, for orders 1–6.
Heptiamond Tri-Oddities. These are like oddities but with ternary symmetry, for order 7.


Polyhex Oddities. Oddities for polyhexes of order up to 5, with specific symmetries.
Hexahex Oddities. Hexahex oddities with specific symmetries.
Heptahex Oddities. Heptahex oddities with specific symmetries.
Polyhex Tri-Oddities. Tri-oddities for polyhexes of order up to 5.
Hexahex Tri-Oddities. Tri-oddities for hexahexes.
Heptahex Tri-Oddities. Tri-oddities for heptahexes.


Tetrapent Oddities. Oddities for tetrapents.
Pentapent Oddities. Oddities for pentapents.
Hexapent Oddities. Oddities for hexapents.
Heptapent Oddities. Oddities for heptapents.


Tetrahept Oddities. Oddities for tetrahepts.
Pentahept Oddities. Oddities for pentahepts.


Polyoct Oddities. Oddities for polyocts of order 1 through 5.


Pentenn Oddities. Oddities for pentenns.


Polydec Oddities. Oddities for polydecs.


Tetrahendec Oddities. Oddities for tetrahendecs.


Polyabolo Oddities. Oddities for polyaboloes.


Polycairo Oddities. Oddities for polycairos.


Polykite Oddities. Oddities for polykites.


Polygem Oddities. Oddities for polygems.


Polyhing Oddities. Oddities for polyhings.


Pentacube Oddities. Full-symmetry oddities for pentacubes.

Back to Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]