A triangle polyomino is a polyomino in the form of an isosceles
right triangle.
It has two straight edges and one zigzag edge
that forms
its hypotenuse.
A triangular prism polycube
is a polycube prism whose base is a triangle polyomino.
Here I show the smallest known triangular prism polycubes that can be tiled with copies of of two different pentacubes, using at least one of each. A prime mark (′) after a letter denotes a mirror image. For example, S′ is the mirror image of S. To see a tiling, click on the corresponding entry in the table below. Missing entries indicate unsolved cases.
If you find a smaller solution, or solve an unsolved case, please write.
See also Tiling Pyramid Prism Polycubes with Two Pentacubes and Tiling Diamond Prism Polycubes with Two Pentacubes.
| A | B | E | E′ | F | G | G′ | H | H′ | I | J | J′ | K | L | M | N | P | Q | R | R′ | S | S′ | T | U | V | W | X | Y | Z | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | 4 | 8 | 18 | 18 | 6 | 20 | 15 | 6 | 4 | 3 | 10 | 4 | 6 | 4 | 12 | 18 | 8 | 15 | 8 | – | 12 | 18 | |||||||
| B | 8 | 18 | 42 | 8 | 10 | 9 | 12 | 6 | 39 | 8 | 6 | 3 | 12 | 8 | 12 | 6 | 8 | 18 | 42 | 4 | 18 | ||||||||
| E | 42 | 8 | 42 | 12 | 4 | 8 | 6 | 8 | 8 | – | 10 | 6 | 6 | 4 | 4 | 6 | 12 | 44 | – | 20 | 6 | 14 | 12 | – | 8 | – | |||
| F | – | 12 | 10 | 12 | – | 12 | – | 42 | 4 | 4 | – | – | – | 44 | 8 | – | – | 12 | – | ||||||||||
| G | – | 12 | 18 | 18 | 9 | 8 | 44 | 4 | – | 4 | 6 | 3 | – | – | – | – | – | 12 | 6 | – | – | 4 | 44 | ||||||
| H | 6 | 6 | 8 | 8 | 6 | 4 | 18 | 15 | 4 | 6 | 18 | 18 | 18 | 6 | 18 | 4 | 12 | 6 | 21 | 6 | 18 | ||||||||
| I | 12 | 12 | 3 | 15 | 10 | 3 | 6 | 15 | 12 | 10 | 10 | 6 | 6 | 10 | 10 | 10 | |||||||||||||
| J | 8 | 8 | 4 | 12 | 8 | 6 | 4 | 8 | 8 | 3 | 9 | 6 | 8 | 6 | 12 | 42 | 8 | 12 | |||||||||||
| K | 10 | – | – | 8 | 4 | 42 | – | – | 12 | 8 | 42 | – | 8 | – | |||||||||||||||
| L | 6 | 6 | 4 | 4 | 4 | 4 | 12 | 8 | 8 | 2 | 15 | 10 | 12 | ||||||||||||||||
| M | – | 8 | 4 | – | – | 44 | 9 | 42 | – | – | 12 | – | |||||||||||||||||
| N | 12 | 8 | 4 | – | 32 | 63 | 12 | 4 | – | 15 | – | ||||||||||||||||||
| P | 4 | 9 | 4 | 8 | 9 | 6 | 3 | 9 | 2 | 12 | |||||||||||||||||||
| Q | 4 | 6 | 8 | 6 | 6 | 6 | 4 | 4 | 8 | ||||||||||||||||||||
| R | – | 6 | – | 42 | 12 | 21 | – | – | 4 | 12 | |||||||||||||||||||
| S | – | – | 44 | 18 | 36 | – | 8 | – | |||||||||||||||||||||
| T | 6 | 16 | 24 | – | 12 | – | |||||||||||||||||||||||
| U | 12 | 18 | – | 6 | 126 | ||||||||||||||||||||||||
| V | 42 | – | 8 | 8 | |||||||||||||||||||||||||
| W | – | 4 | – | ||||||||||||||||||||||||||
| X | 30 | – | |||||||||||||||||||||||||||
| Y | 12 | ||||||||||||||||||||||||||||
| Z | |||||||||||||||||||||||||||||
Last revised 2024-01-08.
