Board Size Classes
Classification by Cell Shape And Dimensions
A Board Size category may be determined by fixing minimum and maximum cells using the formula:
- Min Cells = ((Faces + 1) x (Dimensions(SizeCategory)))
- Max Cells = ((Faces + 1) x (Dimensions(SizeCategory + 1))) - 1
Descriptions for each category might be :
- 0 tiny
- 1 very small
- 2 small
- 3 standard
- 4 large
- 5 very large
- 6 super large
- 7 huge
- 8 extra huge
- 9 super huge
Examples
page_revision: 6, last_edited: 1188472317|%e %b %Y, %H:%M %Z (%O ago)
I tried to use this formula for 4-dimensional boards, and came up with this :
Cell faces : 8 (8 orthogonal directions.)
Dimensions : 4
0 : 0 - 35
1 : 36 - 143
2 : 144 - 575
3 : 576 - 2303
4 : 2304 - 9215
5 : 9216 - 36863
6 : 36864 - 147455
7 : 147456 - 589823
8 : 589824 - 2359295
9 : 2359296 - 9437183
… tesseracts.
terrifying numbers ..
It might also be possible to use this formula for Charles Gilman's Honeycomb Chess, which uses hexagonal prisms.
Well, if I'm doing the numbers right, the 4x4x4x4 is 256 squares, and size 2. This is small, and it seems quite accurate. The 5x5x5x5 is 625; the 6x6x6x6 is 1296: both size 3. 7x7x7x7 is 2401, and size 4, as is 8x8x8x8, at 4096, and 9x9x9x9, at 6561. And 10x10x10x10 is size 5. 20x20x20x20 is 160,000, jumping it to size 7. And 30x30x30x30 is 810,000, for size 8. Terrifying numbers, indeed, but subjectively, they seem pretty accurate to me. It does look like Graeme has come up with a useable size formula that is reasonably generalizeable - congrats to you, Graeme!
I've added an example for the hex-prism board of Honeycomb Chess - an interesting board design, though it would seem that an increase in size might be called for - say 12 ranks x 28 hex-prism-board?