Surface Dissections
Author : Gavin Theobald
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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 - 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 - Three Octahedra (3 pieces)
Tetrahedron - Cube - Octahedron (4 pieces)
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