Tuesday, November 25, 2008


Originally uploaded by thekirbster.
Dave Koski is juggling those Baer cells again, getting cool enneacontahedron dissections. You'll find related reading at George Hart's web sites, also mine, Russell Towle's.

The five Baer cells, all zonohedra constructible with Zome, amalgamate sequentially as convex polyhedra, out to the enneacontahedron.

Dave is noticing the surface : total facet ratios apparently traverse the sequence 1:1, 1:2... 1:8, e.g. the five ways to build a hexahedron involve solo Baer cells, so 1:1, whereas dodecahedra might be assembled seven ways, always from 4 cells (4*6 = 24 facets, 12 on the surface, 12:24 = 1:2 and so on).

Additionally, eight icosahedra, seven rhombic triacontahedra, five with 42 faces, 2 with 56 faces, one with 72 faces, and a final enneacontahedron of 90 faces (the proverbial partridge in a pear tree), all fit into this simple, rational rubric.