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Re: OT hypercube (was: Con-other)

From:John Vertical <johnvertical@...>
Date:Friday, May 30, 2008, 21:23
On Fri, 30 May 2008 15:07:50 -0400, Mark J. Reed wrote:

>In neither case does it matter if the object is solid or hollow. But >if it's not transparent then the drawing degenerates to a square. >Which isn't that exciting. :)
Not necessarily… This is, again, the difference between a direct 2D projection - which could also be a hexagon or an octagon, but indeed flat - and a 2D picture of a 3D projection; which could be eg. a rhombic dodecahedron. You can construct one of those from four skew'd, 3D-Penrose-tile-like pieces. This is the projection equivalent to a cube, viewed corner-on, looking like a hexagon made from three rhombuses (yeah, I'm not even going to try fancy-pluralize that right). …These rhombic parallelepipeds aren't the actual 3D Penrose tiles however; those will produce a rhombic triacontahedron (aka d30) insted. Supposedly, such a construction is a 3D projection of a penteract, but as said, my visualization skills don't go that far. Still, compare with the tesseract-in-octagon construction I described in my previous post; subtract edges that cross one another, and you'll be left with an octagon constructed from squares and rhombuses. Intuition would say that this is an analogical case. John Vertical


Eugene Oh <un.doing@...>