460: Torus

Christmas is just around the corner, so I was thinking “wreath” shapes and stumbled across an astonishing torus made entirely of Tom Hull’s “Phizz” units:

The structure is based on twisted units that combine in 5’s (a pentagon has positive curvature), 6’s (a hexagon has zero curvature) and 7’s (a heptagon has negative curvature).

The inside has 10 heptagons and hexagon spacers, the outer rim has 10 pentagons with hexagon spacers and the rest of the shapes are hexagons.

This shape does my head in – heptagons take up more paper yet less space in the shape … huh? Negative curvature makes the inside of the donut by making a series of “saddles” which is pretty neat. Continue reading

411: Phizz-based Stellated Icosahedron

The “phizz” unit designed by Tom Hull is a basic building block that can be used for many modulars:

I thought I would start manageable, so devised a 30 unit ball, 6 faces each of 5 colours – total of 30 units. These are easy folding and have a positive locking mechanism so were a good choice.

The tricksey part was to ensure an even colour balance – making sure that no face has the same colour twice. that did my head in a little, and it seemd to take me ages to come up with a construction method where I could easily predict what colour next to use.

In the end, a lovely modular – I may try for something grander, we shall see.