The labyrinth ofpolyominoes
  • intro
  • catalog
  • symmetry
  • classes
  • packing
  • tiling
  • genealogy
  • glossary
  • links
Rectangle
Dir44\textrm{Dir}_{4}^{4}Dir44​
Wedge
Dir43\textrm{Dir}_{4}^{3}Dir43​
Staircase
Dir42t\textrm{Dir}_{4}^{2\textrm{t}}Dir42t​
Stack
Dir42c\textrm{Dir}_{4}^{2\textrm{c}}Dir42c​
Fork
Dir41\textrm{Dir}_{4}^{1}Dir41​
Bar chart
Dir32c\textrm{Dir}_{3}^{2\textrm{c}}Dir32c​
Diamond
Dir40\textrm{Dir}_{4}^{0}Dir40​
Wing
Dir31\textrm{Dir}_{3}^{1}Dir31​
Crescent
Dir30\textrm{Dir}_{3}^{0}Dir30​
Antler
Dir2c1\textrm{Dir}_{2\textrm{c}}^{1}Dir2c1​
Range chart
Dir2t0\textrm{Dir}_{2\textrm{t}}^{0}Dir2t0​
Bent tree
Dir2c0\textrm{Dir}_{2\textrm{c}}^{0}Dir2c0​
Tree
Dir10\textrm{Dir}_{1}^{0}Dir10​
Other
Dir00\textrm{Dir}_{0}^{0}Dir00​
Full Table
Classes Tree

Tree polyomino

A polyomino that is orthogonally directed is called a tree.

Note that trees can have “thick roots” (aka cycles) unlike graph theoretical trees.

All other special classes can be built off this one, by restricting to polyominoes that are trees in two or more directions.

Symbol

Dir10\textrm{Dir}_{1}^{0}Dir10​

Regex

ru(ru|lu|ld(ld|rd)*lu)*ld(ld|rd)*

Polyomino list

ruluruldrdluld
9
ruluruldluldrdld
9