Message #1801

From: schuma <mananself@gmail.com>
Subject: 48-cell Shallow cut FT solved using MPUlt
Date: Wed, 29 Jun 2011 00:53:19 -0000

Hi,

I’ve just solved the 48-cell, aka bitruncated 24-cell, with shallow cuts. Note that the only 48-cell FT puzzle defined by Andrey in MPUlt v1.06 is not shallow-cut. The depth of cuts are 0.9 there, creating 95 stickers per cell, some of which are tiny. A shallow-cut one has only 75 stickers per cell. The depth of a shallow-cut FT can be set to any number greater than approximately 0.945. I chose depth = 0.95.

The puzzle is similar to the FT bitruncated simplex, which I solved several days ago. They have the same types of pieces. I didn’t know anything about the truncated polytopes in 4D until recently. Now I appreciate these bitruncated shapes because their cell-transitivity.

The shallow-cut FT 48-cell is a quite large puzzle, containing nontrivial 1200 pieces. In terms of the number of pieces, it’s about half of the mighty 120-cell. I used basically the same method as in the 120-cell. Since there are less cells, I can find a highlighted cell among many colorful cells. So I didn’t change the colors of the stickers. I used 16 hours to solve it, less than 1/3 of the 120-cell.

I noticed a bug for the bitruncated simplex. In the bitruncated simplex there are 10 cells, belonging to two types. Five cells come from the cells of the simplex and the other five come from the vertices. The bug is that an algorithm that is recorded on one type of cells cannot be applied to the other type. So I have to record two identical copies of the same macro for two types of cells. This bug doesn’t exist on the bitruncated 24-cell.

Nan