Polyhex, Polyhing, and Polybrex Oddities

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.

These pages show minimal known oddities and similar constructions for polyhexes, polyhings, and polybrexes.

Standard Oddities

Trihex Oddities. Trihex oddities with specific symmetries.
Tetrahex Oddities. Tetrahex oddities with specific symmetries.
Pentahex Oddities. Oddities for pentahexes, with specific symmetries.
Pentahex Pair Oddities with Full Symmetry. Full-symmetry polyhexes tiled with an odd number of two different pentahexes.
Pentahex Pair Oddities with 6-Rotary Symmetry. Sixfold rotary symmetric polyhexes tiled with an odd number of two different pentahexes.
Pentahex Pair Oddities with Dual Orthogonal Symmetry. Polyhexes with dual orthogonal symmetry tiled with an odd number of two different pentahexes.
One-Sided Pentahex Oddities. Oddities for pentahexes that may not be reflected.
The Magic Pentahex Pair Polyhex Oddity. The same odd polyhex is tiled with 153 different pairs of pentahexes.
Tetrahex-Pentahex Oddities. Full-symmetry polyhexes tiled with an odd number of copies of a tetrahex and a pentahex.
Trihex-Pentahex Oddities. Full-symmetry polyhexes tiled with an odd number of copies of a trihex and a pentahex.
Hexahex Oddities. Hexahex oddities with specific symmetries.
Heptahex Oddities. Oddities for polyhexes with 7 cells, with specific symmetries.
Polyhing Oddities. Oddities for polyhings.
Tribrex Oddities. Oddities for tribrexes.
Tetrabrex Oddities. Oddities for tetrabrexes.

Tri-Oddities

Dihex, Trihex, and Tetrahex Tri-Oddities. Tri-oddities for polyhexes with from 2 to 4 cells.
Pentahex Tri-Oddities. Tri-oddities for pentahexes.
Hexahex Tri-Oddities. Tri-oddities for hexahexes.
Pentahex Pair Tri-Oddities. Tri-oddities for pairs of pentahexes.
Pentahex Pair Tri-Oddities with Horizontal Symmetry. Horizontally symmetric tri-oddities for pairs of pentahexes.
Pentahex Pair Tri-Oddities with Vertical Symmetry. Vertically symmetric tri-oddities for pairs of pentahexes.

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Col. George Sicherman [ HOME | MAIL ]