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.

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Col. George Sicherman [ HOME | MAIL ]