# Surface Dissections

### Author : Gavin Theobald

Solid dissections of various polyhedra of equal volume are generally not possible.
But it is possible to dissect the surfaces of any polyhedra of equal surface area.

In the following diagrams the dotted lines show the edges of each polyhedron.
Sometimes not all edges are shown in an attempt to make clearer the construction
of the dissection.

### Tetrahedron — Cube (2 pieces)

### Tetrahedron — Octahedron (2 pieces)

### Tetrahedron — Dodecahedron (6 pieces)

### Tetrahedron — Icosahedron (2 pieces)

### Tetrahedron — Stellated Octahedron (2 pieces)

### Tetrahedron — Truncated Tetrahedron (2 pieces)

### Tetrahedron — Triangular Prism (2 pieces)

### Tetrahedron — Pentagonal Prism (2 pieces)

### Tetrahedron — Hexagonal Prism (2 pieces)

### Tetrahedron — Square Antiprism (2 pieces)

### Tetrahedron — Pentagonal Antiprism (2 pieces)

### Tetrahedron — Hexagonal Antiprism (2 pieces)

### Tetrahedron — Two Tetrahedra (2 pieces)

### Tetrahedron — Three Tetrahedra (3 pieces)

### Cube — Octahedron (3 pieces)

### Cube — Icosahedron (3 pieces)

### Cube — Two Cubes (2 pieces)

### Octahedron — Icosahedron (3 pieces)

### Octahedron — Two Octahedra (4 pieces)

### Octahedron — Three Octahedra (3 pieces)

### Tetrahedron — Cube — Octahedron (4 pieces)