Tuesday, January 20, 2009

Inaugural Day Ball

Confetti by D. Koski using vZome
David Koski has been working hard on his analysis of the 62-faced great rhombicosidodecahedron in terms of component hexahedra, in turn comprised of edges from the golden cuboid.

These studies relate to Steve Baer's vis-a-vis the 90-faced enneacontahedron, the hexahedral Baer cells likewise expressible in terms of phi-scaled tetrahedral components.

This newest dissection features 455 hexahedra with some of these (70) flattened into tiles, yielding one hexagon and two compositions of three Penrose tiles (two thin and a fat, two fat and a thin), the latter suitable for tiling the 12 decagons.

Additional patterns pertain, relating the axial count to surface:total facet ratios. These patterns served Koski as a guide, when developing this 15 axis shape from a 14 axis precursor, adding 91 hexahedra in the process.

Five of the component hexahedra are simple cubes and in Confetti (above), their locations are depicted. Note that one of these cubes is on the surface. David comments: "The name? First thing to pop in my head. I do like the Obama inaugural celebratory tie in."