Here's how I have always understood it: When making a picture frame, you mitre the corner joints at 45 degrees, and may also wish to bevel the edges to make a more pleasant profile than a plain rectangle. So when making a hollow cube from plywood, you would mitre the edges at 45 deg. and join them a...

The Tao of Stella.

(In the religion of Taoism, "Tao" translates loosely as "way" or "path").

Surely second only in wisdom to The Tao of Pooh.

Well, I guess one man's tool to tell you how to fit tabs inside is another man's interactive tab designer. What I envisage is the ability to move tabs around and check whether they need a bit of trimming or similar. For example it might: * keep track of which edge pairs with which, and insist that j...

The example of the four rectangles is not relevant, because it is not addressing how to fill a single polygon but how to fill in between an arbitrary collection of overlapping polygons. That is a an entirely different issue. By the suggested rule, a smooth morph of a nonconvex figure could indeed re...

In response to Rob, I would suggest that another method is possible. It is not necessary to identify "zero density" with "outside and unfilled". We may define "outside" as any (continuous) region of space which contains infinitely many lines which do not meet our polytope. We then understand interio...

Material: card, 120gsm for small models, thicker for larger ones. Scoring: any blunt point that's handy. Cutting: Craft knife for edges, scissors for tabs (I use the single-tab method). Glue: Bostik. It dries very quickly. Mostly, I spread a thin layer on each surface (using tip of tube and fingers)...

Two more books I would recommend, especially if you are interested in spacefilling polyhedra: Williams; The geometrical foundation of natural structure. Written decades ago in a (then) trendy fixed-pitch typewriter font. But it is still a standard reference for the Archimedean polyhedra and their sp...

It depends on whether you want the dual to be exactly like the one Stella provides (there are various kinds of dual). If you cut the corners off a Platonic polyhedron (truncate it), the cut surfaces are just like the faces of the dual. This is why the cuboctahedron and icosidodecahedron work. If you...

I usually use method (2) - one tab glued under the joining face. It's much the quickest way when it's done right . Also, it offers the most foolproof way to number the assembly sequence, matching Tab 1 to Edge 1, etc. It makes a huge difference (especially to the beginner) how sensibly the tabs are ...

Branko does not list any title "Vertically transitive polyhedra" on the pages linked. Is that the title of the hardcopy you have, or is it called something else? I think it is safe to assume that "vertically transitive" means that all vertices lie within the same symmetry orbit, i.e. they are all eq...

Hi Rob, I bet you only posted this so it would hook me in! ;) I am new to this forum, so I hope I am not repeating stuff the rest of you already know. Like the snub cube (and all uniform polyhedra), this facetting has vertices all alike within its symmetry - we say that it is isogonal. As you say, i...