Any 2 dimensional polygon, such as a square, can be divided in different ways. How one divides, or 'dissects' the shape creates diferent results.

dissecting the square

The pentagon may be dissected as well, which gives us the familiar 5-pointed star:

One may dissect real objects in various ways as well. Cubes dissect space in such a way that they tile space (fill space without any gaps when stacked).


cubes tile space

The tetrahedron does not tile space because there is a gap created when the tetrahedrons are joined. This is due to the phenomenon of a compound angle, as the normal 60 degree inner angle of a triangle is tilted. You can see this when you join 5 tetrahedrons:

MagneBlocks™ tetrahedrons do not tile space


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