| Multiple Dimensions |
| Number of Dimensions | |||||||||||||||
| F
i g u r e s |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
| Point | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 1024 | 2048 | 4096 | ||
| Line | 1 | 4 | 12 | 32 | 80 | 192 | 448 | 1024 | 2304 | 5120 | 11264 | 24576 | |||
| Square | 1 | 6 | 24 | 80 | 240 | 672 | 1792 | 4608 | 11520 | 28160 | 67584 | ||||
| Cube | 1 | 8 | 40 | 160 | 560 | 1792 | 5376 | 15360 | 42240 | 112640 | |||||
| Tesseract | 1 | 10 | 60 | 280 | 1120 | 4032 | 13440 | 42240 | 126720 | ||||||
| ? | 1 | 12 | 84 | 448 | 2016 | 8064 | 29568 | 101376 | |||||||
| ? | 1 | 14 | 112 | 672 | 3360 | 14784 | 80256 | ||||||||
| ? | 1 | 16 | 144 | 960 | 5280 | 25344 | |||||||||
| ? | 1 | 18 | 180 | 1320 | 7920 | ||||||||||
| ? | 1 | 20 | 220 | 1760 | |||||||||||
| ? | 1 | 22 | 264 | ||||||||||||
| ? | 1 | 24 | |||||||||||||
| ? | 1 | ||||||||||||||
A point has 0 dimensions. There is nothing you can measure on it. It is made up of 1 point.
A line has 1 dimension. You can measure its length. It is made up of 1 line and 2 points (the ends). You make a line by translating a point through the first dimension.
A square has 2 dimensions. You can measure its length and width. It is made up of 1 square, 4 lines (the sides), and 4 points (the corners). You make a square by translating a line through the second dimension.
A cube has 3 dimensions. You can measure it's length, width, and height. It is made up of 1 cube, 6 squares (the sides), 12 lines (the edges), and 8 points (the corners). You make a cube by translating a square through the third dimension.
A tesseract has 4 dimensions. This is where our experience lets us down, even though the math of it still holds up. The columns in the chart above show how many of the lower order figures make up a tesseract. You make a tesseract by translating a cube through the fourth dimension.
And so on. Words begin to fail in the description of higher order
figures, but the math keeps on going forever.