### Triangular prism — Cube (10 pieces)

### Pentagonal prism — Cube (10 pieces)

### Hexagonal prism — Cube (8 pieces)

Starting with the prism, this dissection can be performed with
just five straight cuts.

The dissection is translational.

### Heptagonal prism — Cube (11 pieces)

### Octagonal prism — Cube (10 pieces)

Unfortunately the shaded piece is very thin in the middle, so there is room for
improvement here.

### Truncated octahedron — Cube (11 pieces)

Starting with the truncated octahedron, this dissection can be performed with
just four straight cuts.

The dissection is translational.

### Rhombic dodecahedron — Cube (11 pieces)

### Stellated rhombic dodecahedron — Cube (12 pieces)

### Truncated octahedron — Rhombic dodecahedron (24 pieces)

### Stellated rhombic dodecahedron — Truncated octahedron (6 pieces)

The dissection is translational and hingeable.

### Stellated rhombic dodecahedron — Rhombic dodecahedron (24 pieces)

### Cube — 2 Tetrahedra + Octahedron (15 pieces)

Starting with the cube, this dissection can be performed with
just five straight cuts.

The dissection is translational.

### Rhombic triacontahedron — Cube (29 pieces)

We start by dividing the rhombic triacontahedron into 5 pieces. If it has a
volume of 1 then the five pieces have volumes of 0.4, 0.2, 0.2, 0.1 and 0.1.

The four small pieces with volumes of 0.2, 0.2, 0.1 and 0.1 are rearranged into
a single block.

The first cut adds 4 pieces. These pieces are rearranged.
The second cut adds a further 5 pieces. Again rearrange the pieces
into a clean parallel sided block.
A final two parallel cuts are made adding a single piece and 5 more pieces.
The pieces are now rearranged to give a final block of dimensions 0.6×1×1.
The pieces required are 4+4+5+(1+5) for a total of 19 pieces.

Here are these 19 pieces shown separately and grouped for the original 4 pieces.

The central block must now be dissected.
We start by making 3 parallel cuts making a total of 4 pieces. These are rearranged.
Now another cut is made adding 3 more pieces. Again rearrange the pieces making a
clean parallel sided block.
A final cut is made adding a further 3 pieces.
The pieces are now rearranged to give a final block of dimensions 0.4×1×1.
The pieces required are 4+3+3 for a total of 10 pieces.

The two blocks of 0.4×1×1 and 0.6×1×1 can now be combined to
make a cube with a total of 29 pieces

Here are these 10 pieces shown separately.