# Message #918

From: Andrey <andreyastrelin@yahoo.com>

Subject: Rectangular 3^6

Date: Fri, 18 Jun 2010 05:35:30 -0000

I thought a little about fractal implementation of 3^6, but it seems to be even less regular than 3^7. What we need is to show painted 3^6 cube. It’s not difficult to show painted "main" faces - but now we decompose the cube by secondary dimensions first - so it will look like 27 painted 3^3s (and every 3d "sticker" represents one cubie of 3^6 - but actual main stickers are 2d now). But then we need to show colors of parts of secondary faces. I see place for them around the main cube - somethis like cloud of small squares parallel to each face. It may be one layer of squares (6*3^2*3^2) - if we show secondary faces of one layer of cubies only - or 3 layers (6*3^3*3^2) arranged like sides of 4D puzzle 9x9x9x3. Looks difficult.

Another idea - to show two cubes with different division to main/secondary dimensions: one cube shows main faces and another - secondary (and they have different arrangement of cubies). I can imagine even 3^9 implemented this way (it will look like 2187 Ribik’s cubes 3^3 arranged in 3 cubes 9x9x9). What is good there - we don’t need spacing between stickers on the deepest level. And we spend only 2 triangles for each sticker (instead of 12). But if we try to make 7D or 8D this way then third view will be very strange: for 3^7 it will look like 9^3 cube of bi-colored objects (segments with painted ends, or coins with painted sides, or just pairs or parallel squares). May be for 3^7 it will be better not to show 14-th face. For 3^8 third view will consist of 3^2 Rubik’s cubes (prisms 3x3x1 with 4 painted sides).

May be it will be better than 4D-like interface. I don’t know.

Andrey