Monday, February 23, 2009

From PolyList

by D. Koski using vZome
Well, I was encouraged by Scott Vothmann to try again on the great rhombicuboctahedron.

I didn't exactly succeed but did generate this 132 sided rhombic form. It has 48 squares and 24 (60,120) rhombi and the three other rhombi I have not identified yet. 12 of the fattest one, 24 each of the ones that make the eight pointed stars.

I figured the form out by using the Parallel Projection Process. Vorthmann's vZome has a root 2 system which has 24 brown strut positions or 12 different axes.

So, 12*11 will be the amount of rhombic faces of which there are five different types. Therefore, 12/1*11/2*10/3 = 220 total hexahedral cells.

Yes, those are flat hexagons and there are 4 zero volume hexahedra that correspond to them.

Amounts of different hexahedra will soon follow.

BTW, The late Russell Towle refers to the Archimedean Truncated Cuboctahedron (s/b Great Rhombicuboctahedron?) on this page: scroll down to middle of page

He calls it A Notorious Zonohedron, does anyone know why?

Is this shape cataloged anywhere, I would like to find more out about it.

David Koski
Minneapolis MN

Followup to PolyList: I made a mistake. There are not 48 squares, but they are rhombi of course. David Koski