http://i709.photobucket.com/albums/ww94/SteveGarrison/14.jpg

This may or may not be assembled in the proper sequence. There are many ways to assemble the 4 types of polyhedra without gaps. Apparently there is a sequence where the crystal can be assembled endlessly without voids or overlapping ...

With all four polyhedra in memories, I started with a rhombohedron and augmented a Bilinski dodecahedron to 3 faces...
http://i709.photobucket.com/albums/ww94/SteveGarrison/3.jpg

Continued augmenting rhombohedra, and Bilinski dodecahedra forming a cavity for the center of the quasicrystal which ...

The trick is to choose the right slices through the 3D object. It is easiest to explain for the cube.

Pick one vertex and identify the three adjacent ones. Cut round these three to remove a triangular pyramid. Do the same on the opposite side so you now have two pyramids and a square antiprism ...

Yes, both the rhombohedra I describe have this property - the one with the golden rhombs lengthways, the other with them sideways.

Are you any good at geometry and basic algebra? It is reasonably easy to develop formulas for the stretch/shrink ratios.

Then feed the formula into a high-precision ...

There are two kinds of rhombohedron, depending on whether you stretch or squash the cube along a diagonal. Once the two rhombohedra are scaled to the same edge length, all your figures can be assembled from copies of just these two, and in this respect they bear a close parallel to the original ...

Update. I realized I could use non-uniform scaling to stretch a cube along a 3-fold axis by a factor of 1.851229520935533 to make the square faces into golden rhombi for a Golden Rhombohedron. I arrived at this scale factor by process of elimination (my 7th grade math teacher would have called this ...

Hello everyone. I'm trying to figure out how to make 2 more polyhedrons in addition to the rhombic triacontahedron and rhombic icosahedron. These 4 different shapes are augmented together in various ways in a non-periodic fashion to form a model of a quasicrystal which has no gaps and has true 5 ...

I have not tried gluing the 1/4 inch pine plywood, but I have glued a test joint from 1/2 inch birch plywood, and it was plenty strong using original Titebond glue on the beveled edges. I think that the thinner plywood could be glued without reinforcing tabs and be reasonably strong. If tabs were ...

I came up with a good way to make polyhedrons out of wood and wanted to show them here. I have a few spheres made from hardwood, and the flat-faced models are 1/4" plywood that has been taped together and then stretch-wrapped. Sure is a lot of fun! I really like the Great Stella program.

Steve ...