The opposite faces of these cobblestones are identical parallelograms. The twelve edges are divided into three groups of four edges parallel and of same length.
On each of the eight vertices the sum of the three angles must be less than 360°; if this condition is not satisfied faces overlap on the drawing here with and the parallelepiped doesn't exist ! We get these hexahedra by stretching or compressing a rectangular parallelepiped along one of its diagonals (so we get the rhombohedra starting from a cube). There exists two kinds of non rectangular parallelepipeds:

 
Three acute angles on two opposite vertices (a, b, c around the yellow point); on each of the six other vertices only one angle is acute.
The condition of existence is  bc  < a < b+c 
Three obtuse angles on two opposite vertices (a, b, c around the yellow point); on each of the six other vertices only one angle is obtuse.
The condition of existence is simply a+b+c < 360°  
You may move the red points with your mouse to change the shape of the net.
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convex polyhedra  non convex polyhedra  interesting polyhedra  related subjects  April 2002 updated 01072002 