A 3x3x3 solid can be filled with four copies of a tetracube and two copies of
a pentacube, with one cube left unfilled.
Below is a catalog of the tetracube/pentacube pairs for which solutions exist.
These are qualified by the placement of the monocube, which can be in one of
four placements, arbitrarily labeled here as A, B, C, or D. For example, the
first set shown below, the combination of
four S-tetracubes and two U-pentacubes,
has only one solution, and that has the monocube placed at A. Similarly,
four square-tetracubes and two Z-pentacubes
can only be solved with the monocube at D.
Many sets can be solved with the monocube at different places. For example,
four left screw-tetracubes and two L4-pentacubes
can be solved with the monocube at two different positions, but has the nice
property that the solution is unique for each such placement.
The catalog links to solution drawings whenever there are five or fewer for a
particular monocube placement. For example, to see the solutions for
four t-tetracubes and two L3-pentacubes,
click the solution drawings link. In the
bottom half of the linked window you will see a frame for each solution.
Within the frame you can click on the next (or previous) link to add (or
remove) a piece from the drawing.
1: 4 S-tetracubes, 2 U-pentacubes
1 solution for A
4× 
2× 
solution drawings
2: 4 T-tetracubes, 2 L4-pentacubes
1 solution for A
4× 
2× 
solution drawings
3: 4 T-tetracubes, 2 V-pentacubes
1 solution for B
4×
2× 
solution drawings
4: 4 T-tetracubes, 2 Q-pentacubes
1 solution for B
4×
2× 
solution drawings
5: 4 L-tetracubes, 2 X-pentacubes
1 solution for C
4× 
2× 
solution drawings
6: 4 square-tetracubes, 2 Z-pentacubes
1 solution for D
4× 
2× 
solution drawings
7: 4 T-tetracubes, 2 X-pentacubes
1 solution for D
4×
2×
solution drawings
8: 4 branch-tetracubes, 2 P-pentacubes
1 solution for D
4× 
2× 
solution drawings
9: 4 left screw-tetracubes, 2 L4-pentacubes
1 solution for A and 1 solution for B
4× 
2×
solution drawings
10: 4 T-tetracubes, 2 F-pentacubes
1 solution for B and 1 solution for D
4×
2× 
solution drawings
11: 4 T-tetracubes, 2 Z-pentacubes
1 solution for B and 1 solution for D
4×
2×
solution drawings
12: 4 L-tetracubes, 2 T-pentacubes
1 solution for B, 1 solution for C and 2 solutions for D
4×
2× 
solution drawings
13: 4 T-tetracubes, 2 L2-pentacubes
1 solution for A and 2 solutions for B
4×
2× 
solution drawings
14: 4 T-tetracubes, 2 L3-pentacubes
1 solution for A and 4 solutions for B
4×
2× 
solution drawings
15: 4 L-tetracubes, 2 L4-pentacubes
1 solution for D, many solutions for A, many solutions for B and many solutions for C
4×
2×
solution drawings
16: 4 L-tetracubes, 2 N1-pentacubes
1 solution for D, many solutions for A, many solutions for B and many solutions for C
4×
2× 
solution drawings
17: 4 square-tetracubes, 2 L2-pentacubes
2 solutions for A
4×
2×
solution drawings
18: 4 branch-tetracubes, 2 U-pentacubes
2 solutions for A
4×
2×
solution drawings
19: 4 square-tetracubes, 2 P-pentacubes
2 solutions for D
4×
2×
solution drawings
20: 4 S-tetracubes, 2 P-pentacubes
2 solutions for D
4×
2×
solution drawings
21: 4 S-tetracubes, 2 W-pentacubes
2 solutions for D
4×
2× 
solution drawings
22: 4 S-tetracubes, 2 Z-pentacubes
2 solutions for D
4×
2×
solution drawings
23: 4 T-tetracubes, 2 P-pentacubes
2 solutions for A, 2 solutions for D and 6 solutions for B
4×
2×
solution drawings
24: 4 L-tetracubes, 2 W-pentacubes
2 solutions for C, 3 solutions for A and 6 solutions for B
4×
2×
solution drawings
25: 4 T-tetracubes, 2 U-pentacubes
2 solutions for C and 4 solutions for B
4×
2×
solution drawings
26: 4 L-tetracubes, 2 T1-pentacubes
2 solutions for A and many solutions for C
4×
2× 
solution drawings
27: 4 S-tetracubes, 2 L2-pentacubes
3 solutions for A
4×
2×
solution drawings
28: 4 L-tetracubes, 2 A-pentacubes
3 solutions for D, many solutions for A, many solutions for B and many solutions for C
4×
2× 
solution drawings
29: 4 L-tetracubes, 2 Z-pentacubes
4 solutions for C, 5 solutions for B, 7 solutions for A and many solutions for D
4×
2×
solution drawings
30: 4 L-tetracubes, 2 V-pentacubes
4 solutions for B and 7 solutions for C
4×
2×
solution drawings
31: 4 L-tetracubes, 2 U-pentacubes
4 solutions for D, many solutions for A, many solutions for B and many solutions for C
4×
2×
solution drawings
32: 4 left screw-tetracubes, 2 P-pentacubes
5 solutions for A and 6 solutions for B
4×
2×
solution drawings
33: 4 L-tetracubes, 2 F-pentacubes
5 solutions for C and many solutions for A
4×
2×
solution drawings
34: 4 L-tetracubes, 2 L1-pentacubes
many solutions for C
4×
2× 
35: 4 left screw-tetracubes, 2 V-pentacubes
many solutions for B
4×
2×
36: 4 L-tetracubes, 2 L3-pentacubes
many solutions for A and many solutions for C
4×
2×
37: 4 L-tetracubes, 2 T2-pentacubes
many solutions for A and many solutions for C
4×
2× 
38: 4 L-tetracubes, 2 V1-pentacubes
many solutions for A and many solutions for C
4×
2× 
39: 4 L-tetracubes, 2 L2-pentacubes
many solutions for A, many solutions for B and many solutions for C
4×
2×
40: 4 L-tetracubes, 2 N2-pentacubes
many solutions for A, many solutions for B and many solutions for C
4×
2× 
41: 4 L-tetracubes, 2 P-pentacubes
many solutions for A, many solutions for B, many solutions for C and many solutions for D
4×
2×
42: 4 L-tetracubes, 2 Q-pentacubes
many solutions for A, many solutions for B, many solutions for C and many solutions for D
4×
2×