I know how to create parallelepiped and combine them to form a parallelepiped tiling, but the tiles overlap...
I started with this code:
P1 = Graphics3D[{GeometricTransformation[{Opacity[.85], Red,
Cuboid[]}, ShearingMatrix[Pi/4, {1, 0, 0}, {-1, 1, 0}]]},
Boxed -> False]
P2 = Graphics3D[{GeometricTransformation[{Opacity[.85], Red,
Cuboid[]}, ShearingMatrix[Pi/4, {1, 0, 0}, {-1, 1, 0}]]},
Boxed -> False]
P3 = Graphics3D[{GeometricTransformation[{Opacity[.85], Red,
Cuboid[]}, ShearingMatrix[Pi/4, {1, 0, 0}, {-1, 1, 0}]]},
Boxed -> False]
Show[P1,P2,P3]
I don't know how to fix the positions of the parallelepipeds (I prefer different shapes) so that they will not overlap and no gaps between them.
P1
:Graphics3D[ NestList[GeometricTransformation[#, TranslationTransform[{1/2, 3/2, 0}]] &, First@P1, 5], Boxed -> False]
Istvan's answer shows a better way to build up the tiles. $\endgroup$ – rm -rf♦ Jan 16 '14 at 20:33