Re: [math-fun] Zonohedral surfaces
Not at all. My answer was the result of very deep thought! —Dan Jim Propp wrote: ----- I was just overlooking the obvious! -----
If we insist on Stewart's "aplanar" property (faces that share an edge may not be coplanar) then I think it can still be done. Take a rhombic dodecahedron, or a rhombic triacontahedron, and select any antipodal pair of parallel rhombic faces. Drill a tunnel from one of the pair to the other. The four faces of the tunnel will be rectangles. On Thu, Oct 22, 2020 at 5:45 PM Dan Asimov <dasimov@earthlink.net> wrote:
Not at all. My answer was the result of very deep thought!
—Dan
Jim Propp wrote: ----- I was just overlooking the obvious! -----
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Or take the eight cube solution and skew two opposite cubes so the visible parts are not rectangles. This introduces the necessary separating edges. On Thu, Oct 22, 2020 at 3:05 PM Allan Wechsler <acwacw@gmail.com> wrote:
If we insist on Stewart's "aplanar" property (faces that share an edge may not be coplanar) then I think it can still be done. Take a rhombic dodecahedron, or a rhombic triacontahedron, and select any antipodal pair of parallel rhombic faces. Drill a tunnel from one of the pair to the other. The four faces of the tunnel will be rectangles.
On Thu, Oct 22, 2020 at 5:45 PM Dan Asimov <dasimov@earthlink.net> wrote:
Not at all. My answer was the result of very deep thought!
—Dan
Jim Propp wrote: ----- I was just overlooking the obvious! -----
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I like this. Here are interactive images of a rhombic dodecahedron and a rhombic triacontahedron: https://www.karzes.com/polyhedra/polyhedron.html?ph=V3.4.3.4 https://www.karzes.com/polyhedra/polyhedron.html?ph=V3.5.3.5 If you have a mouse (rather than a touchscreen), you can click-and-drag to manually rotate them. Tom Allan Wechsler writes:
If we insist on Stewart's "aplanar" property (faces that share an edge may not be coplanar) then I think it can still be done. Take a rhombic dodecahedron, or a rhombic triacontahedron, and select any antipodal pair of parallel rhombic faces. Drill a tunnel from one of the pair to the other. The four faces of the tunnel will be rectangles.
participants (4)
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Allan Wechsler -
Dan Asimov -
Tom Karzes -
Tomas Rokicki