Rubiksfication of non-chiral faceted Even Order N-icons

For faceted non-chiral Even Order N-icons, if the number of longitudes is equal to N, there are equal internal polygons on the x, y, and z axes. This allows freedom of movement on three planes instead of the normal one plane of N-icons in general. This is on the same order as working with a 2x2x2 Rubik's Cube.

The requirement is that N mod 4 = 0. The number of longitudes (or meridians) M must equal N. When N = 4 the result is an octahedron.

The standard globe of the Earth that you've often seen is one such case. It is divided into 10 degree increments latitudinally and longitudinally. The top half of the globe could be turned on the equator 90 degrees. Then it could turned 90 degrees on the prime meridian, and yet another 90 degrees at 90 degree longitude mark.

There are additional degrees of freedom when the faceted non-chiral Even Order N-icon is in the initial solved state or Twist 0. These would be along every line of latitude, such that each layer of polygons could be rotated around the X axis. This would also be the case if the initial twist was 180° on the XY plane or a twist of N/2. For example, N36+T18 would have the same latitudinal degree of freedom as the base model of N36+T0. If such a device could be built with this additional feature and a map or pattern was displayed on the surface, once jumbled it would be very difficult to solve.

The pictures shown below are models in LiveGraphics3D

N36+T0 Solved State off   solid   transparent   switch	N36+T9 90° twist off   solid   transparent   switch	180° twist on the ZX Plane off   solid   transparent   switch	180° twist on the YZ Plane off   solid   transparent   switch

Question or comments about the web page should be directed to polyhedra@bigfoot.com.

The generation of OFF, VRML, and Live3D files was done with Antiprism. The Hedron application by Jim McNeill was used to generate VRML Switch files.

History:

2007-09-06 Initial Release

Roger's Polyhedra, (c) 2006, Roger Kaufman