Sunday, October 22, 2006

Playing with Blocks

David Koski's dissection of a cube
into phi-scaled T-mods + remainder tets
David brought some cardboard models along for the Portland Knowledge Lab to play with, including his dissection of the cube into blue, yellow and green T-mods, plus a few remainder tets.

Scale any T-mod's edges by phi (about 1.618) to get the next larger size, or by 1/phi (about .618) to get the next smaller size. Volume changes as a third power of the scale factor, surface area as a second power.

The remainder tet is what's left when you build a T-mod recursively from phi-scaled smaller versions of itself. The T-mod is 1/120th of a rhombic triacontahedron.

Note on nomenclature: the E-mod has the same angles (shape) as the T-mod in Synergetics, but a different surface:volume ratio as it's slightly bigger. The T-mod has the same volume as the A- and B-mods in Fuller's concentric hierarchy (1/24). David does not feel bound to use this accounting system however.

a PKL tableau
From PKL we walked to nearby Lucky Lab for brews then headed back to Meliptus for a higher tide experience, which included an interesting tour of George's decommissioned army tug boat (George, a WWII pilot, is 81 and lives on this tug).

David and George discuss
mechanical matters
aboard George's tug
New Era