The Cylindrical Cone
The cylindrical cone, or cylindrone for short, is constructed by tapering a 3D cone along the W-axis.
I had a question about this, and PM'd him, but he didn't seem to see it, and he has no e-mail anywhere. So I figured I could ask publicly, and he or others could answer.
Do you mean "tapering a 3D cylinder along the w-axis"? Because that is what the object shown and discussed there is. I had been thinking about what a conic hypercone (cone tapered along the W-axis) would be like, and I figured the circular base extruded and shrank down to a point would generate another cone. So you would have two cones sharing a common circular base, and ending in two separate apices, joined by a ridge (the extruded original apex, and all enveloped by a triangular torus). I wondered why I didn't see this on your site anywhere, and then I realized that the object you have here is the opposite of this: 2 cones sharing a common apex, with separate circular bases joined by a cylinder. This would be a cylinder extruded and tapered down to a point, not a cone. So this is truly a cylindrone, but what is described is not cylindrical at all, but rather duo-conic: a single circular base in the x and y axes, tapered to points along both the z and w axes.
Anyway, this stuff is fascinating; and I have been studying your page to know more about the duocycles. Before; all my knowledge of the 4th dimension was confined to the simpler "regular" objects.
Eric B