A pyramid polyomino is a polyomino in the form of an isosceles
right triangle.
It has two zigzag edges
and one straight edge that forms
its hypotenuse.
A pyramid prism polycube
is a polycube prism whose base is a pyramid polyomino.
Here I show the smallest known pyramid 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 Triangular 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 | 10 | 16 | 20 | 40 | 10 | 18 | 10 | 10 | 10 | 10 | 10 | 9 | 10 | 10 | 20 | 20 | 20 | 16 | 16 | 80 | 16 | 20 | |||||||
| B | 15 | 16 | 16 | 9 | 9 | 4 | 16 | 9 | 25 | 15 | 9 | 9 | 16 | 16 | 16 | 4 | 15 | 16 | 30 | 16 | 20 | ||||||||
| E | 30 | 30 | 30 | 30 | 10 | 16 | 9 | 15 | 15 | 15 | 15 | – | 10 | 9 | 9 | 20 | 15 | 80 | 80 | 50 | 15 | 20 | 10 | – | 9 | 80 | |||
| F | – | 20 | 9 | 15 | – | 16 | – | 40 | 10 | 10 | – | – | – | 10 | 20 | – | – | 16 | – | ||||||||||
| G | – | 10 | 40 | 32 | 15 | 15 | 40 | 10 | – | 20 | 10 | 10 | – | – | – | 40 | 60 | 8 | 18 | – | – | 9 | 80 | ||||||
| H | 10 | 9 | 15 | 15 | 10 | 10 | 80 | 20 | 10 | 10 | 40 | 10 | 40 | 10 | 20 | 10 | 15 | 10 | 36 | 10 | 80 | ||||||||
| I | 9 | 25 | 4 | 16 | 9 | 4 | 9 | 16 | 18 | 9 | 9 | 9 | 9 | 9 | 9 | 16 | |||||||||||||
| J | 15 | 15 | 10 | 20 | 15 | 8 | 10 | 15 | 15 | 10 | 15 | 15 | 15 | 15 | 15 | 20 | 15 | 15 | |||||||||||
| K | 16 | – | – | 20 | 10 | – | – | – | 20 | 20 | 40 | – | 9 | – | |||||||||||||||
| L | 16 | 16 | 10 | 8 | 10 | 10 | 16 | 15 | 20 | 10 | 9 | 20 | 18 | ||||||||||||||||
| M | – | 20 | 10 | – | 80 | – | 15 | – | – | – | 9 | – | |||||||||||||||||
| N | 30 | 10 | 40 | 40 | 48 | 30 | 18 | 10 | – | 16 | – | ||||||||||||||||||
| P | 10 | 10 | 10 | 9 | 9 | 15 | 10 | 9 | 9 | 20 | |||||||||||||||||||
| Q | 10 | 20 | 20 | 10 | 15 | 20 | 10 | 8 | 20 | ||||||||||||||||||||
| R | – | 80 | 80 | 36 | 10 | 20 | – | – | 9 | 80 | |||||||||||||||||||
| S | – | – | 20 | 32 | 40 | – | 20 | – | |||||||||||||||||||||
| T | 15 | 30 | 36 | – | 20 | – | |||||||||||||||||||||||
| U | 20 | 30 | 60 | 8 | 60 | ||||||||||||||||||||||||
| V | 15 | – | 16 | 20 | |||||||||||||||||||||||||
| W | – | 16 | – | ||||||||||||||||||||||||||
| X | 20 | – | |||||||||||||||||||||||||||
| Y | 20 | ||||||||||||||||||||||||||||
| Z | |||||||||||||||||||||||||||||
Last revised 2024-02-09.
