(wikipedia.org)

This research is what I’m researching in Cecil Balmond’s and Ezio Blasetti’s studio now. The basic ASCII files are from Ezio Blasetti. For next generation’s recursive, we have to need the information about each cell’s vertices’ index so that we can get each cell’s centroid.

 

Because of the dual attributes, each solid can convert to be the dual geometry by connecting the centroids of the cells. Like 120-cell has 120 cells and 120 centroids. As for 600-cell, the dual geometry of 120-cell, has exactly 120 vertices. So if you connect the 120 centroids of 120-cell, you can get a 600-cell.

 

The basic ASCII files includes all the cell vertices’ index. We added five geometries’ cell information,5-cell which is also called simplex, 8-cell, 16-cell, 120-cell and 600-cell. For 5-cell, 24-cell, it is very easy to do the combinations like this:

5-cell vertices index: 0,1,2,3,4

5 cells’ vertices index:

cell 0:(0,1,2,3,4)

cell 1:(0,1,2,3,5)

cell 2:(0,1,2,4,5)

cell 3:(0,1,3,4,5)

cell 4:(1,2,3,4,5)

 

The 8-cell’s and 16-cell’s combinations are researched by Wei Chen. The 120-cell’s and 600-cell’s are based on Dr. Ing Libor Vasa’s research, which you can find on his homepage here: http://meshcompression.org/

 

You can write your own ‘readfile’ component by using Grasshopper+Python and can choose whether you need the cell’s information or not.

 

Files are like this and I will share you the files at the end of this page.

#5-cell source file

5
0 0 0 2
-1.11803 1.11803 1.11803 -0.5
1.11803 -1.11803 1.11803 -0.5
1.11803 1.11803 -1.11803 -0.5
-1.11803 -1.11803 -1.11803 -0.5
10
2 3
3 4
4 2
1 3
4 1
1 2
0 3
4 0
0 2
0 1
10
3 2 3 4
3 1 3 4
3 1 2 4
3 1 2 3
3 0 3 4
3 0 2 4
3 0 2 3
3 0 1 4
3 0 1 3
3 0 1 2

 

#8-cell source file w/t cell index info

16
-1 -1 -1 -1
-1 -1 -1 1
-1 -1 1 -1
-1 -1 1 1
-1 1 -1 -1
-1 1 -1 1
-1 1 1 -1
-1 1 1 1
1 -1 -1 -1
1 -1 -1 1
1 -1 1 -1
1 -1 1 1
1 1 -1 -1
1 1 -1 1
1 1 1 -1
1 1 1 1
32
0 2
2 3
3 1
1 0
0 4
4 5
5 1
4 6
6 2
0 8
8 9
9 1
8 10
10 2
8 12
12 4
6 7
7 5
7 3
10 11
11 3
9 11
9 13
13 5
12 13
12 14
14 10
14 6
14 15
15 13
15 11
15 7
24
4 0 2 3 1
4 0 4 5 1
4 0 4 6 2
4 0 8 9 1
4 0 8 10 2
4 0 8 12 4
4 4 6 7 5
4 2 6 7 3
4 1 5 7 3
4 2 10 11 3
4 1 9 11 3
4 1 9 13 5
4 8 10 11 9
4 8 12 13 9
4 8 12 14 10
4 4 12 13 5
4 4 12 14 6
4 2 10 14 6
4 12 14 15 13
4 10 14 15 11
4 9 13 15 11
4 6 14 15 7
4 5 13 15 7
4 3 11 15 7

 

#8-cell source file w/ cell index info

16
-1 -1 -1 -1
-1 -1 -1 1
-1 -1 1 -1
-1 -1 1 1
-1 1 -1 -1
-1 1 -1 1
-1 1 1 -1
-1 1 1 1
1 -1 -1 -1
1 -1 -1 1
1 -1 1 -1
1 -1 1 1
1 1 -1 -1
1 1 -1 1
1 1 1 -1
1 1 1 1
32
0 2
2 3
3 1
1 0
0 4
4 5
5 1
4 6
6 2
0 8
8 9
9 1
8 10
10 2
8 12
12 4
6 7
7 5
7 3
10 11
11 3
9 11
9 13
13 5
12 13
12 14
14 10
14 6
14 15
15 13
15 11
15 7
24
4 0 2 3 1
4 0 4 5 1
4 0 4 6 2
4 0 8 9 1
4 0 8 10 2
4 0 8 12 4
4 4 6 7 5
4 2 6 7 3
4 1 5 7 3
4 2 10 11 3
4 1 9 11 3
4 1 9 13 5
4 8 10 11 9
4 8 12 13 9
4 8 12 14 10
4 4 12 13 5
4 4 12 14 6
4 2 10 14 6
4 12 14 15 13
4 10 14 15 11
4 9 13 15 11
4 6 14 15 7
4 5 13 15 7
4 3 11 15 7
8
8 0 1 2 3 4 5 6 7
8 0 1 2 3 8 9 10 11
8 0 1 4 5 8 9 12 13
8 0 2 4 6 8 10 12 14
8 8 9 10 11 12 13 14 15
8 4 5 6 7 12 13 14 15
8 2 3 6 7 10 11 14 15
8 1 3 5 7 9 11 13 15

 

#16-cell source file w/ cell index info

8
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 -1
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
24
5 6
6 7
7 5
4 6
7 4
4 5
0 6
7 0
0 5
1 6
7 1
1 4
0 1
2 5
7 2
2 4
0 2
1 2
3 5
6 3
3 4
0 3
1 3
2 3
32
3 5 6 7
3 4 6 7
3 4 5 7
3 4 5 6
3 0 6 7
3 0 5 7
3 0 5 6
3 1 6 7
3 1 4 7
3 1 4 6
3 0 1 7
3 0 1 6
3 2 5 7
3 2 4 7
3 2 4 5
3 0 2 7
3 0 2 5
3 1 2 7
3 1 2 4
3 0 1 2
3 3 5 6
3 3 4 6
3 3 4 5
3 0 3 6
3 0 3 5
3 1 3 6
3 1 3 4
3 0 1 3
3 2 3 5
3 2 3 4
3 0 2 3
3 1 2 3
16
4 4 5 6 7
4 0 1 2 3
4 4 5 6 3
4 0 1 2 7
4 4 5 2 7
4 0 1 6 3
4 4 1 6 7
4 0 5 2 3
4 0 5 6 7
4 4 1 2 3
4 4 5 2 3
4 0 1 6 7
4 4 1 6 3
4 0 5 2 7
4 4 1 2 7
4 0 5 6 3

 

120-cell and 600-cell would be incredibly long. If you need them to do the research please download them.

 

 

4D-Platonic-Solids